Improved Regret for Efficient Online Reinforcement Learning with Linear Function Approximation

Uri Sherman, Tomer Koren, Yishay Mansour
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:31117-31150, 2023.

Abstract

We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions. We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses. Our algorithm obtains an $\widetilde O(K^{6/7})$ regret bound, improving significantly over previous state-of-the-art of $\widetilde O (K^{14/15})$ in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of $\widetilde O (K^{2/3})$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-sherman23a, title = {Improved Regret for Efficient Online Reinforcement Learning with Linear Function Approximation}, author = {Sherman, Uri and Koren, Tomer and Mansour, Yishay}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {31117--31150}, 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/sherman23a/sherman23a.pdf}, url = {https://proceedings.mlr.press/v202/sherman23a.html}, abstract = {We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions. We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses. Our algorithm obtains an $\widetilde O(K^{6/7})$ regret bound, improving significantly over previous state-of-the-art of $\widetilde O (K^{14/15})$ in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of $\widetilde O (K^{2/3})$.} }
Endnote
%0 Conference Paper %T Improved Regret for Efficient Online Reinforcement Learning with Linear Function Approximation %A Uri Sherman %A Tomer Koren %A Yishay Mansour %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-sherman23a %I PMLR %P 31117--31150 %U https://proceedings.mlr.press/v202/sherman23a.html %V 202 %X We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions. We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses. Our algorithm obtains an $\widetilde O(K^{6/7})$ regret bound, improving significantly over previous state-of-the-art of $\widetilde O (K^{14/15})$ in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of $\widetilde O (K^{2/3})$.
APA
Sherman, U., Koren, T. & Mansour, Y.. (2023). Improved Regret for Efficient Online Reinforcement Learning with Linear Function Approximation. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:31117-31150 Available from https://proceedings.mlr.press/v202/sherman23a.html.

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