Non-stationary Reinforcement Learning under General Function Approximation

Songtao Feng, Ming Yin, Ruiquan Huang, Yu-Xiang Wang, Jing Yang, Yingbin Liang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:9976-10007, 2023.

Abstract

General function approximation is a powerful tool to handle large state and action spaces in a broad range of reinforcement learning (RL) scenarios. However, theoretical understanding of non-stationary MDPs with general function approximation is still limited. In this paper, we make the first such an attempt. We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs, which subsumes majority of existing tractable RL problems in static MDPs as well as non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA, which features a sliding window mechanism and a new confidence set design for non-stationary MDPs. We then establish an upper bound on the dynamic regret for the proposed algorithm, and show that SW-OPEA is provably efficient as long as the variation budget is not significantly large. We further demonstrate via examples of non-stationary linear and tabular MDPs that our algorithm performs better in small variation budget scenario than the existing UCB-type algorithms. To the best of our knowledge, this is the first dynamic regret analysis in non-stationary MDPs with general function approximation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-feng23e, title = {Non-stationary Reinforcement Learning under General Function Approximation}, author = {Feng, Songtao and Yin, Ming and Huang, Ruiquan and Wang, Yu-Xiang and Yang, Jing and Liang, Yingbin}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {9976--10007}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/feng23e/feng23e.pdf}, url = {https://proceedings.mlr.press/v202/feng23e.html}, abstract = {General function approximation is a powerful tool to handle large state and action spaces in a broad range of reinforcement learning (RL) scenarios. However, theoretical understanding of non-stationary MDPs with general function approximation is still limited. In this paper, we make the first such an attempt. We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs, which subsumes majority of existing tractable RL problems in static MDPs as well as non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA, which features a sliding window mechanism and a new confidence set design for non-stationary MDPs. We then establish an upper bound on the dynamic regret for the proposed algorithm, and show that SW-OPEA is provably efficient as long as the variation budget is not significantly large. We further demonstrate via examples of non-stationary linear and tabular MDPs that our algorithm performs better in small variation budget scenario than the existing UCB-type algorithms. To the best of our knowledge, this is the first dynamic regret analysis in non-stationary MDPs with general function approximation.} }
Endnote
%0 Conference Paper %T Non-stationary Reinforcement Learning under General Function Approximation %A Songtao Feng %A Ming Yin %A Ruiquan Huang %A Yu-Xiang Wang %A Jing Yang %A Yingbin Liang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-feng23e %I PMLR %P 9976--10007 %U https://proceedings.mlr.press/v202/feng23e.html %V 202 %X General function approximation is a powerful tool to handle large state and action spaces in a broad range of reinforcement learning (RL) scenarios. However, theoretical understanding of non-stationary MDPs with general function approximation is still limited. In this paper, we make the first such an attempt. We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs, which subsumes majority of existing tractable RL problems in static MDPs as well as non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA, which features a sliding window mechanism and a new confidence set design for non-stationary MDPs. We then establish an upper bound on the dynamic regret for the proposed algorithm, and show that SW-OPEA is provably efficient as long as the variation budget is not significantly large. We further demonstrate via examples of non-stationary linear and tabular MDPs that our algorithm performs better in small variation budget scenario than the existing UCB-type algorithms. To the best of our knowledge, this is the first dynamic regret analysis in non-stationary MDPs with general function approximation.
APA
Feng, S., Yin, M., Huang, R., Wang, Y., Yang, J. & Liang, Y.. (2023). Non-stationary Reinforcement Learning under General Function Approximation. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:9976-10007 Available from https://proceedings.mlr.press/v202/feng23e.html.

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