Policy Evaluation for Reinforcement Learning from Human Feedback: A Sample Complexity Analysis

Zihao Li, Xiang Ji, Minshuo Chen, Mengdi Wang
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2737-2745, 2024.

Abstract

A recently popular approach to solving reinforcement learning is with data from human preferences. In fact, human preference data are now used with classic reinforcement learning algorithms such as actor-critic methods, which involve evaluating an intermediate policy over a reward learned from human preference data with distribution shift, known as off-policy evaluation (OPE). Such algorithm includes (i) learning reward function from human preference dataset, and (ii) learning expected cumulative reward of a target policy. Despite the huge empirical success, existing OPE methods with preference data often lack theoretical understandings and rely heavily on heuristics. In this paper, we study the sample efficiency of OPE with human preference and establish a statistical guarantee for it. Specifically, we approach OPE with learning the value function by fitted-Q-evaluation with a deep neural network. By appropriately selecting the size of a ReLU network, we show that one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Under the assumption of high reward smoothness, our results almost align with the classical OPE results with observable reward data. To the best of our knowledge, this is the first result that establishes a provably efficient guarantee for off-policy evaluation with RLHF.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-li24l, title = {Policy Evaluation for Reinforcement Learning from Human Feedback: A Sample Complexity Analysis}, author = {Li, Zihao and Ji, Xiang and Chen, Minshuo and Wang, Mengdi}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2737--2745}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/li24l/li24l.pdf}, url = {https://proceedings.mlr.press/v238/li24l.html}, abstract = {A recently popular approach to solving reinforcement learning is with data from human preferences. In fact, human preference data are now used with classic reinforcement learning algorithms such as actor-critic methods, which involve evaluating an intermediate policy over a reward learned from human preference data with distribution shift, known as off-policy evaluation (OPE). Such algorithm includes (i) learning reward function from human preference dataset, and (ii) learning expected cumulative reward of a target policy. Despite the huge empirical success, existing OPE methods with preference data often lack theoretical understandings and rely heavily on heuristics. In this paper, we study the sample efficiency of OPE with human preference and establish a statistical guarantee for it. Specifically, we approach OPE with learning the value function by fitted-Q-evaluation with a deep neural network. By appropriately selecting the size of a ReLU network, we show that one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Under the assumption of high reward smoothness, our results almost align with the classical OPE results with observable reward data. To the best of our knowledge, this is the first result that establishes a provably efficient guarantee for off-policy evaluation with RLHF.} }
Endnote
%0 Conference Paper %T Policy Evaluation for Reinforcement Learning from Human Feedback: A Sample Complexity Analysis %A Zihao Li %A Xiang Ji %A Minshuo Chen %A Mengdi Wang %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-li24l %I PMLR %P 2737--2745 %U https://proceedings.mlr.press/v238/li24l.html %V 238 %X A recently popular approach to solving reinforcement learning is with data from human preferences. In fact, human preference data are now used with classic reinforcement learning algorithms such as actor-critic methods, which involve evaluating an intermediate policy over a reward learned from human preference data with distribution shift, known as off-policy evaluation (OPE). Such algorithm includes (i) learning reward function from human preference dataset, and (ii) learning expected cumulative reward of a target policy. Despite the huge empirical success, existing OPE methods with preference data often lack theoretical understandings and rely heavily on heuristics. In this paper, we study the sample efficiency of OPE with human preference and establish a statistical guarantee for it. Specifically, we approach OPE with learning the value function by fitted-Q-evaluation with a deep neural network. By appropriately selecting the size of a ReLU network, we show that one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Under the assumption of high reward smoothness, our results almost align with the classical OPE results with observable reward data. To the best of our knowledge, this is the first result that establishes a provably efficient guarantee for off-policy evaluation with RLHF.
APA
Li, Z., Ji, X., Chen, M. & Wang, M.. (2024). Policy Evaluation for Reinforcement Learning from Human Feedback: A Sample Complexity Analysis. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2737-2745 Available from https://proceedings.mlr.press/v238/li24l.html.

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