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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf,len=755
+page_content='Reinforcement Learning from Diverse Human Preferences  Wanqi Xue * 1 Bo An 1 Shuicheng Yan 2 Zhongwen Xu 2  Abstract  The complexity of designing reward functions  has been a major obstacle to the wide application  of deep reinforcement learning (RL) techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Describing an agent’s desired behaviors and prop-  erties can be difficult, even for experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' A new  paradigm called reinforcement learning from hu-  man preferences (or preference-based RL) has  emerged as a promising solution, in which reward  functions are learned from human preference la-  bels among behavior trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' However, ex-  isting methods for preference-based RL are lim-  ited by the need for accurate oracle preference  labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' This paper addresses this limitation by de-  veloping a method for crowd-sourcing preference  labels and learning from diverse human prefer-  ences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The key idea is to stabilize reward learning  through regularization and correction in a latent  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' To ensure temporal consistency, a strong  constraint is imposed on the reward model that  forces its latent space to be close to the prior distri-  bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Additionally, a confidence-based reward  model ensembling method is designed to generate  more stable and reliable predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The pro-  posed method is tested on a variety of tasks in  DMcontrol and Meta-world and has shown con-  sistent and significant improvements over existing  preference-based RL algorithms when learning  from diverse feedback, paving the way for real-  world applications of RL methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Introduction  Recent advances in reinforcement learning (RL) have  achieved remarkable success in simulated environments  such as board games (Silver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Moravˇc´ık  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2017) and video games (Mnih et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Vinyals  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Wurman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' However, the application  This work was done during an internship at Sea AI  Lab, Singapore 1Nanyang Technological University, Singapore  2Sea AI Lab, Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Correspondence to:  Wanqi Xue  <wanqi001@e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='ntu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='sg>, Zhongwen Xu <xuzw@sea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='com>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Preprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  of RL to real-world problems remains a challenge due to  the lack of a suitable reward function (Leike et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  On the one hand, designing a reward function to provide  dense and instructive learning signals is difficult in complex  real-world tasks (Christiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  On the other hand, RL agents are likely to exploit a reward  function by achieving high return in an unexpected and un-  intended manner (Leike et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ouyang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  To alleviate the problems, preference-based RL is proposed  to convey human-preferred objectives to agents (Christiano  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Stiennon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2020), in which a (human)  teacher is requested to provide his/her preferences over pairs  of agents’ historical trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Based on human feedback,  a reward model is learned and applied to provide learning  signals to agents (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 1(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Preference-based RL pro-  vides an effective way to learn from human intentions, rather  than explicitly designed rewards, and has demonstrated its  effectiveness in areas such as robotics control (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=',  2021b) and dialogue systems (Ouyang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Though promising, the learning of preference-based RL  heavily relies on plenty of expert feedback, which could  be prohibitively expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Existing works typically focus  on feedback-efficient algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' They investigate several  sampling and exploration strategies with the aim of finding  the most deserving queries to be labelled (Biyik & Sadigh,  2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Some other  works improve feedback efficiency by learning good policy  initialization with imitation learning (Ibarz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018) and  unsupervised pre-training (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In addition,  semi-supervised reward learning is also used for better effi-  ciency (Park et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Although these methods reduce  the demand for human feedback, scaling preference-based  RL to large-scale real-world problems is still difficult be-  cause the need for feedback increases significantly with the  complexity of problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Recently, there has been a trend to replace expensive expert  feedback with crowd-sourced data for scalability (Gerst-  grasser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ouyang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' For example,  in ChatGPT, a group of annotators are hired for providing  affordable human feedback to RL agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The impressive  results show that preference-based RL has great potential  when sufficient human feedback is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Obtaining hu-  man feedback from various sources can effectively address  the issue of data scarcity in preference-based RL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' However,  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='11774v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='LG]  27 Jan 2023  Reinforcement Learning from Diverse Human Preferences  Annotation  Reward learning  Encoder  Decoder  (a)  (b)  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Illustration of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' (a) There is a team of different annotators with bounded rationality to provide their preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Based on the preference data, a reward model is learned and used to provide rewards to an RL agent for policy optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' (b) The  reward models encode an input into a latent space where a strong distribution constraint is applied to address inconsistency issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Following that, a novel reward model ensembling method is applied to the decoders to aggregate their predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  this approach also brings some challenges, as the collected  preferences may be unreliable, inconsistent, or even adver-  sarial, making it difficult to optimize the policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The diverse  nature of the feedback can make it challenging to deter-  mine the true underlying preferences and to learn from them  effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  In this paper, we propose a simple yet effective method to  help existing preference-based RL algorithms learn from  diverse human preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The key idea is to stabilize the  reward learning by regularizing and correcting its predic-  tions in a latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Concretely, we first map the inputs  of the reward model to a latent space, enabling the predicted  rewards to be easily manipulated by varying them in this  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Second, to ensure temporal consistency throughout  the learning process, we impose a strong constraint on the  latent space by forcing it to be close to a prior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  This prior distribution serves as a reference point, providing  a way to measure the consistency of the predicted rewards  over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Lastly, we measure the confidence of the re-  ward model in its predictions by calculating the divergence  between its latent space and the prior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Based  on this divergence, we design a confidence-based reward  model ensembling method to generate more stable and reli-  able predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We demonstrate the effectiveness of our  method on a variety of complex locomotion and robotic  manipulation tasks from DeepMind Control Suite (DM-  Control) (Tassa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Tunyasuvunakool et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2020)  and Meta-world (Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The results show that  our method is able to effectively recover the performance  of existing preference-based RL algorithms under diverse  preferences in all the tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Preliminaries  We consider the reinforcement learning (RL) framework  which is defined as a Markov Decision Process (MDP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' For-  mally, an MDP is defined by a tuple ⟨S, A, r, P, γ⟩, where  S and A denote the state and action space, r(s, a) is the  reward function, P(s′|s, a) denotes the transition dynam-  ics, and γ ∈ [0, 1) is the discount factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' At each timestep  t, the agent receives the current state st ∈ S from the  environment and makes an action at ∈ A based on its  policy π(at|st).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Subsequently, the environment returns a  reward rt and the next state st+1 to the agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' RL seeks  to learn a policy such that the expected cumulative return,  E  ��∞  k=0 γkr(st+k, at+k)  �  , is maximized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  In realistic applications, designing the reward function to  capture human intent is rather difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Preference-based  RL is therefore proposed to address this issue by learning  a reward function from human preferences (Akrour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=',  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Wilson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Christiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ibarz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Specifically, there is a human teacher indi-  cating his/her preferences over pairs of segments (σ0, σ1),  where a segment is a part of the trajectory of length H, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=',  σ = {(s1, a1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' , (sH, aH)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The preferences y could  be (0, 1), (1, 0) and (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='5), where (0, 1) indicates σ1 is  preferred to σ0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', σ1 ≻ σ0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' (1, 0) indicates σ0 ≻ σ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  and (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='5) implies an equally preferable case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Each feed-  back is stored as a triple (σ0, σ1, y) in a preference buffer  Dp = {((σ0, σ1, y))i}N  i=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  To learn a reward function ˆr from the labeled preferences,  similar to most prior work (Ibarz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=',  2021b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Park et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=" Hejna III &  Sadigh, 2022), we define a preference predictor by following  (s, a, r(s, a), s')(s, a, s')AReinforcement Learning from Diverse Human Preferences  the Bradley-Terry model (Bradley & Terry, 1952):  Pψ  �  σ1 ≻ σ0�  =  exp  ��H  t=1 ˆr  �  s1  t, a1  t;" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψ  ��  �  i∈{0,1} exp  ��H  t=1 ˆr  �  si  t, ai  t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψ  ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  (1)  Given the preference buffer Dp, we can train the reward  function ˆr by minimizing the cross-entropy loss between the  preference predictor and the actually labeled preferences:  Ls = −  E  (σ0,σ1,y)∼Dp  �  y(0) log Pψ  �  σ0 ≻ σ1�  + y(1) log Pψ  �  σ1 ≻ σ0��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  (2)  where y(0) and y(1) are the first and second element of y,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' With the learned rewards, we can optimize a  policy π using any RL algorithm to maximize the expected  return (Christiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Preference-based Reinforcement Learning  from Diverse Human Feedback  Preference-based RL provides an effective framework to  deliver human intentions to RL agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In this section, we  present our algorithm which helps RL agents to learn from  human preferences that possess high diversity and incon-  sistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The key idea of our algorithm is to stabilize the  reward learning by regularizing and correcting it in a latent  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Specifically, we first map the input of the reward  model to a latent space so that the predicted reward can  be easily manipulated by modifying it in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Second, to achieve temporal consistency throughout the  learning process, we impose a strong constraint on the latent  space by forcing it to be close to a prior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Last,  we measure the confidence of a reward model in its predic-  tion by calculating the divergence between its latent space  and the prior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Based on the divergence, we de-  sign a confidence-based reward model ensembling method  to generate more reliable and stable predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The overall  framework of our algorithm is presented in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Manipulating Rewards within a Latent Space  Reward learning is a key problem in preference-based RL  because RL agents rely on the guidance of the learned re-  ward model for policy optimization (Silver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  However, learning an instructive and stable reward model  is rather difficult when human preferences possess high  diversity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' If we simply minimize the loss in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 2, the  generated rewards will have severe fluctuations and incon-  sistencies because the supervised signal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', the collected  preferences (y), can be noisy, self-contradictory, or even  adversarial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As a result, RL agents cannot converge to a rea-  sonable policy since the learning objectives always change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Algorithm 1 RL from Diverse Human Preferences  1: Input: Strength of constraint φ, number of reward mod-  els N, frequency of feedback session K  2: Initialize parameters of policy π(s, a) and the reward  model ˆr(s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψ)  3: Initialize preferences buffer Dp ← ∅ and replay buffer  Dr ← ∅  4: for each iteration do  5:  if iteration % K == 0 then  6:  Sample (σ0, σ1) and query annotators for y  7:  Store preference Dp ← Dp ∪ {(σ0, σ1, y)}  8:  for each reward model updating step do  9:  Sample a minibatch of preferences (σ0, σ1, y)  10:  Optimize the reward model (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 7)  11:  end for  12:  end if  13:  for each timestep do  14:  Collect s′ by taking action a ∼ π(s, a)  15:  Store transition Dr ← Dr ∪ {(s, a, s′)}  16:  end for  17:  for each policy updating step do  18:  Sample a minibatch of transitions (s, a, s′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  19:  Measure the confidence of reward models (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 8)  20:  Relabel the transitions with ˆr(s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψ) (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 9)  21:  Update the policy π(s, a) on {(s, a, ˆr(s, a), s′)}  22:  end for  23: end for  To deal with the problem, an intuitive solution is to correct  the predicted rewards before feeding them to the agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Con-  ventionally, methods such as reward shaping involve adding  additional rewards or penalties to the original rewards to  guide the agent toward the desired behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' However, the  added rewards usually introduce unintended side effects or  inconsistencies in the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As a mitigation, we  propose to manipulate the rewards within a latent space,  which avoids directly changing the predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We adopt  an encoder-decoder structure where the encoder is used to  map the input, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', a state-action pair, to latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' After  sampling a representation vector from the latent space, the  decoder is applied to map the vector back to a reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Formally, the encoder p(z|s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψe), parameterized by ψe, is  in the form of  p(z|s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψe) = N(z|f µ(s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψe), f Σ(s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψe)),  (3)  where N(µ, Σ) denotes a Gaussian distribution with mean  vector µ and covariance matrix Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The encoder consists of  two multi-layer perceptrons (MLPs) whose output gener-  ates the K-dimensional mean µ and the K × K covariance  matrix Σ, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The decoder d(r|z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψd), with pa-  rameters ψd, takes as input a sampled latent variable z and  outputs a reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Such an encoder-decoder structure enjoys  Reinforcement Learning from Diverse Human Preferences  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Examples for locomotion tasks and robotic manipulation  tasks we test on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  benefits under diverse human preferences: i) we can control  the fluctuations of the rewards by adjusting the distribution  of the latent space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ii) the confidence of the reward model  to its predictions can be easily measured by calculating the  divergence between different latent spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In the following  sections, we will elaborate on how to leverage the aforemen-  tioned advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Achieving Consistency by Imposing a Strong  Constraint  As previously mentioned, the reward model is learned under  the supervision of human feedback, which could have high  diversity if they are collected from different crowds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As a  consequence, the rewards will demonstrate severe fluctua-  tions and inconsistencies throughout the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  For example, at the beginning of the training, the reward  model learns some patterns, and the policy is optimized to-  ward the corresponding objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As the training processes,  more labeled preferences are added to the dataset and the  updated reward model can be completely different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As a  result, the reward model will make distinct predictions for  the same input at the different training stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We found  that it is the temporal inconsistency that causes the collapse  of a policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' To alleviate the problem, we propose to impose  a constraint on the latent space so that the reward model  has a fixed optimization direction throughout the training  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Concretely, we assume that the latent space fol-  lows a prior distribution r(z), and we try to minimize the  Kullback-Leibler (KL) divergence between the latent space  and its prior:  Lc = E(s,a)  �  KL(p(z|s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψe)||r(z))  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  (4)  Since r(z) is pre-defined, the optimization of the encoder  will be guided toward a fixed direction, independent of how  diverse the human preferences are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Minimizing the loss in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 4 is equivalent to  minimizing the mutual information between (S, A) and Z,  which leads to a concise representation of the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Proof: To simplify the notation, we let variable X denote the  input pairs (S, A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Then by the definition of KL-divergence:  Lc =  ��  dx dz p(x)  �  p(z|x) log p(z|x)  r(z)  �  =  ��  dx dz p(x, z) log p(z|x) −  �  dz p(z) log r(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  (5)  Since KL(p(z)|r(z)) ≥ 0, we have  �  dz p(z) log p(z) ≥  �  dz p(z) log r(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As a result,  Lc ≥  ��  dx dz p(x, z) log p(z|x) −  �  dz p(z) log p(z)  = I(Z, X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  (6)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 6 shows that minimizing Lc is equivalent to minimizing  an upper bound of I(Z, X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Overall, the loss function for the reward model is  L = φ ∗ Lc + Ls,  (7)  where φ is a parameter controlling the strength of the con-  straint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Conventionally, φ is set as a small value to confirm  that the supervised signals will not be dominated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' However,  counterintuitively, we found that a large φ is crucial for  good performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Larger φ will lead to a stronger con-  straint on the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As a result, the latent space for  different inputs will be similar, and the predicted rewards  will be controlled into a smaller range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Considering that it  is relative values of rewards, not absolute values, that affect  a policy, a reward model with a smaller value range can  lead to more accurate, stable, and effective outcomes, and  therefore benefit the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Confidence-based Reward Model Ensembling  It is common that diverse human preferences contain out-  lier data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' To reduce the influence of a single data point on  the reward model, we adopt reward model ensembling to  reduce overfitting and improve stability (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Instead of simply averaging, we design  a confidence-based ensembling mechanism to improve per-  formance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The key idea is to aggregate the predicted results  by up-weighting the reward models with higher confidence  and down-weighting those with less confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We first  measure the confidence level of each reward model and then  perform a weighted summation to generate the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Specifically, the confidence of a reward model is measured  by calculating the KL divergence from the predicted latent  space to its prior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' If the KL divergence is small  which means the reward model cannot tell too much input-  specific information, the reward model has low confidence  about the input (a model tends to output the prior directly  Reinforcement Learning from Diverse Human Preferences  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
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+page_content=' Learning curves on locomotion tasks (first row) and robotic manipulation tasks (second row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The locomotion tasks are measured  on the ground truth episode return while the robotic manipulation tasks are measured on the success rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The solid line and shaded  regions represent the mean and standard deviation, respectively, across five runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  if it knows nothing about the input).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' On the contrary, a  large KL divergence indicates a high confidence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We  assume that the confidence is proportional to the exponent  of the KL divergence:  Gi(s, a) =  exp(KL(pi(z|s, a)||r(z)))  �N  j=1 exp(KL(pj(z|s, a)||r(z)))  ,  (8)  where Gi(s, a) denotes the confidence of the i-th reward  model to an input (s, a), N is the number of reward mod-  els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' After determining the confidence of each model, we  calculate the reward by:  ˆr(s, a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ψ) =  N  �  i=1  Gi(s, a) ×  �  di ◦ qi(r|s, a)  �  ,  (9)  where di and qi are the decoder and the encoder of the i-th  reward model, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' With the reword model, we  can use any preference-based RL algorithm to learn the  policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The full procedure of our method is summarized in  Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Experiments  We conduct experiments to answer the following questions:  Q1: Whether the proposed method can effectively help ex-  isting preference-based RL algorithms to learn from  diverse preferences?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Q2: How does each component of the method contribute to  the effectiveness?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Q3: How will latent spaces affect the predicted rewards?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Q4: How will the method be affected by the number of  annotators?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Setup  We evaluate our method on several complex locomotion  tasks and robotic manipulation tasks from DeepMind Con-  trol Suite (DMControl) (Tassa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Tunyasuvu-  nakool et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2020) and Meta-world (Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2020), respec-  tively (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In order to justify the effectiveness of our  method, we train an agent to solve the tasks without observ-  ing the true rewards from the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Instead, several  scripted annotators are generated to provide their prefer-  ences between two trajectory segments for the agent to learn  its policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Unlike existing preference-based RL algorithms  which interact with a single perfect scripted teacher (Chris-  tiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Park et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022), we  consider the situation where there is a team of different an-  notators with bounded rationality to provide the preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Despite being imperfect, the annotators’ preferences are  also calculated from ground truth rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Therefore, we  can quantitatively evaluate the method by measuring the  true episode return or success rate from the environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Our method can be integrated into any preference-based  RL algorithm to recover their performance under diverse  preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In our experiments, we choose one of the most  popular approaches, PEBBLE (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021b), as the  backbone algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We examine the performance of PEB-  BLE under i) a perfect scripted teacher who provides the  ground true feedback (oracle);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ii) a team of randomly sam-  pled annotators whose feedback is imperfect and anisotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  The goal of our method is to recover the performance of  PEBBLE under the annotators as much as possible, to ap-  Reinforcement Learning from Diverse Human Preferences  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
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+page_content='0M  Environment Steps  0  25  50  75  100  Hammer  = 1  = 10  = 100  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ablation study on the strength of the latent space constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The locomotion tasks (first row) are measured on the ground  truth episode return while the robotic manipulation (second row) tasks are measured on the success rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The results show the mean and  standard deviation averaged over five runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  proach the oracle case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Simulating the annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We generate the bounded ratio-  nal scripted annotators by following the previous stochastic  preference model (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021a):  P  �  σ1 ≻ σ0�  =  exp  �  β �H  t=1 γH−tr  �  s1  t, a1  t  ��  �  i∈{0,1} exp  �  β �H  t=1 γH−tr  �  si  t, ai  t  ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  (10)  r(s, a) is the ground truth reward provided by the envi-  ronment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' A scripted annotator is determined by a tuple  ⟨β, γ, ϵ, δequal⟩: β is the temperature parameter that con-  trols the randomness of the stochastic preference model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  An annotator becomes perfectly rational and deterministic  as β → ∞, whereas β = 0 produces uniformly random  choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' γ controls the myopic (short-sighted) behavior of  an annotator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Annotators with small γ will emphasize more  on immediate rewards and down-weight long-term return.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' ϵ  describes the probability that an annotator makes a mistake,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', we flip the preference with the probability of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' δequal de-  notes the threshold that an annotator marks the segments as  equally preferable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', an annotator provides (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='5) as a  response if | �  t r(s1  t, a1  t) − �  t r(s0  t, a0  t)| ≤ δequal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Practi-  cally, we sample a tuple from β ∈ {∞, 1, 5}, γ ∼ U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='8, 1),  ϵ ∼ U(0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='2), δequal ∼ U(0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='2) to generate a scripted an-  notator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' For each task, we randomly generate 100 annotators  to provide feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Each annotator has the same probabil-  ity of being selected for annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Implementation details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' For all tasks, we use the same  hyperparameters used by PEBBLE, such as learning rates,  architectures of the neuron networks, and reward model  updating frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We adopt an uniform sampling strat-  egy, which selects queries with the same probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' At  each feedback session, a batch of 256 trajectory segments  (σ0, σ1) is sampled for annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The strength of con-  straint φ is set as 100 for all tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' For simplicity, we set the  prior distribution of the latent space as standard Gaussian  where the KL-divergence from a latent space to its prior can  be easily calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' All experimental results are reported  with the mean and standard deviation across five runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Experimental Results  Locomotion tasks from DMControl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  We select three  complex environments from DMControl,  which are  Walker walk, Cheetah run, and Quadruped walk, to eval-  uate our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As previously mentioned, PEBBLE is  used as the backbone algorithm and our method is com-  bined with PEBBLE to recover its performance under di-  verse human preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The first row of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 3 shows the  learning curves of PEBBLE and our method when learning  from bounded rational annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We can find that, com-  pared to learning from a single perfect teacher (oracle), the  performance of PEBBLE (measure on true episode return)  decreases dramatically in all three tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' For example, in  Walker walk, PEBBLE is able to achieve 1000 scores if  it learns from a single expert, whereas the value is nearly  half of the preferences are from different annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Such  failures show that existing preference-based RL algorithms  do not work well when the provided preferences contain  diversity and inconsistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' After integrating our method  (the red line), we can find significant performance increases  in all three tasks: our method is able to achieve almost the  same performance as the oracle in Walker walk, while the  performance gap between our method and its upper bound  Reinforcement Learning from Diverse Human Preferences  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Analysis about the influence of φ on the reward model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' First row: increasing the strength of the constraint will narrow the  value range of the predicted rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The reward model will also generate more distinct predictions if φ is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Second row: the t-SNE  visualization of the latent vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' A large φ leads to a more compact and concise pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  (oracle) is very narrow in Cheetah run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In Quadruped walk,  PEBBLE is unable to learn a feasible policy, while our  proposed method still achieves near-optimal performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Robotic manipulation tasks from Meta-world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Meta-  world consists of 50 tasks that cover a range of fundamental  robotic manipulation skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We consider three challenging  environments to evaluate the effectiveness of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  The performance is measured on success rate, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', if the  trained agent is able to successfully finish a task or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Fig 3  (second row) shows the learning curves of our method as  the baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We can find that there is a significant perfor-  mance increase after integrating our method into PEBBLE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  The performance can be almost restored to approach the  oracles in Button Press and Hammer, while in Sweep Into,  the improvement is also non-trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' These results again  demonstrate that our proposed method is able to effectively  help the existing preference-based RL algorithms learn from  diverse preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ablation and Analysis  Effects of the latent space constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As previously in-  troduced, to achieve temporal consistency and set a fixed  optimization direction for the reward model, our method  imposes a constraint on the latent space by forcing its dis-  tribution to be close to the prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' To justify the effect of  the constraint, we implement our method with different  strengths of constraint on all six tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 4,  there is a significant and consistent improvement in all the  tasks as we gradually increase the strength of the constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  For example, in Cheetah run, when we set the strength of  0  100K  200K  300K  400K  500K  Environment Steps  0  200  400  600  800  1000  Episode Return  w/ ensembling  w/o ensembling  0  100K  200K  300K  400K  500K  Environment Steps  0  200  400  600  800  1000  KL-based  mean  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ablation study on reward model ensembling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Left:  Learning curves of Walker walk with and without reward model  ensembling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Right: Learning curves of Walker walk with KL-  based model ensembling and simply averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The results show  the mean and standard deviation averaged over five runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  constraint ψ to 1, 10, and 100, the performance increases  from around 200 to 400 and finally reaches near 600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' This  phenomenon is a little bit counter-intuitive because, con-  ventionally, a too strong constraint is likely to misguide  the reward model and prevent it from learning from super-  vised signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' However, we found that a strong constraint on  the latent space is compulsory to help an agent learn from  diverse feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Analysis about the reward model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' To understand why a  strong constraint is crucial for the performance, we ana-  lyze the effect of the latent space constraint on the reward  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Specifically, we collect 100,000 state-action pairs  from Cheetah run at different training stages and use the  reward model trained with different strengths of constraint  to predict the rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The predictions are presented in  Φ=l  Φ=10  Φ= 100  Predicted Rewards  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
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+page_content=' Learning curves of Cheetah run (a locomotion task) with preferences provided by a different number of annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The results  are measured on the ground truth episode return, with the solid line and shaded regions representing the mean and standard deviation,  respectively, across five runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  the first row of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We can find that as we increase the  strength of constraint, the range of reward values decreases  gradually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' For example, when φ = 1, the predicted rewards  are between -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='6 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='15, while the range is narrowed to  [−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='5, 0] when we set φ = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Moreover, the predicted  rewards are more distinct when φ becomes larger, which  indicates that only really good state-action pairs are given  high rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We also use t-SNE (Van der Maaten & Hin-  ton, 2008) to visualize the latent vector of those state-action  pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 5 (second row), the distribution of the  embeddings becomes more compact as we increase φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Fur-  thermore, the pattern of the embeddings is more clear and  more concise when φ is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Effects of reward model ensembling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We investigate how  well the reward ensembling affects the performance of  our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 6 (left) shows the learning curves of  Walker walk with and without reward model ensembling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  We can find that there is a clear performance drop if using a  single reward model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The results demonstrate that ensem-  bling the predictions of several models is helpful to stabilize  the training process if the preferences are diverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' We fur-  ther investigate whether the proposed KL-based aggregation  method is better than simply averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 6  (right), simply averaging will suffer severe fluctuations in  the training process, while the performance of our method  is significantly more stable and consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Responses to the number of annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' To examine how  will our algorithm respond to the number of annotators, we  implement Cheetah run with preferences provided by dif-  ferent numbers of annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' As shown in Fig 7, when  there is only one annotator which is bounded rational, both  PEBBLE and our method perform worse than the oracle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In  these cases, the preferences are not diverse but just partially  correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' If we slightly increase the number of annotators  to ten, which introduces some diversity, our method is able  to achieve obvious improvement over PEBBLE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The per-  formance gain becomes quite significant when there are  one hundred annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The experiments demonstrate that  our method is suitable for situations where the provided  preferences are diverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Related Work  The main focus in the paper is on one promising direction  which utilizes human preferences (Akrour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Chris-  tiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ibarz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Leike et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Lee  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ouyang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Park et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Liang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022) to perform policy optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Christiano  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' (2017) introduced modern deep learning techniques  to preference-based learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Since the learning of the re-  ward function, modeled by deep neural networks, requires  a large number of preferences, recent works have typically  focused on improving the feedback efficiency of a method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  PEBBLE (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021b) proposed a novel unsupervised  exploration method to pre-train the policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' SURF (Park  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022) adopted a semi-supervised reward learning  framework to leverage a large number of unlabeled samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Some other works improved data efficiency by introducing  additional types of feedback such as demonstrations (Ibarz  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2018) or non-binary rankings (Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In  addition to that, designing intrinsic rewards to encourage  effective exploration is also investigated (Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Despite being efficient, previous methods mainly focus on  learning from a single expert, which will severely limit the  scalability of an algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In this work, we focus on learn-  ing from human preferences collected from different types  of annotators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Our method emphasizes addressing the issue  of diversity rather than feedback efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Conclusion  In this work, we propose a simple yet effective method  to improve the performance of preference-based RL algo-  rithms under diverse feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' The method maps inputs to  a latent space imposes a constraint on the latent space to  Reinforcement Learning from Diverse Human Preferences  maintain temporal consistency, and uses a confidence-based  ensembling method to generate more stable predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Ex-  tensive experiments are conducted in various environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  The results show that our method can significantly improve  performance under diverse preferences in all the tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  References  Akrour, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', Schoenauer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=', and Sebag, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Preference-  based policy learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In Joint European Conference  on Machine Learning and Knowledge Discovery in  Databases, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 12–27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Springer, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Biyik, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' and Sadigh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Batch active preference-based  learning of reward functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' In Conference on Robot  Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' 519–528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Bradley, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' and Terry, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' Rank analysis of incom-  plete block designs: I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content=' the method of paired comparisons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Biometrika, 39(3/4):324–345, 1952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
+page_content='  Cao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49FKT4oBgHgl3EQfSC3u/content/2301.11774v1.pdf'}
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