Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping

Dongruo Zhou, Jiafan He, Quanquan Gu
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:12793-12802, 2021.

Abstract

Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low dimensional space. In this paper, we study reinforcement learning for discounted Markov Decision Processes (MDPs), where the transition kernel can be parameterized as a linear function of certain feature mapping. We propose a novel algorithm which makes use of the feature mapping and obtains a ˜O(d√T/(1−γ)2) regret, where d is the dimension of the feature space, T is the time horizon and γ is the discount factor of the MDP. To the best of our knowledge, this is the first polynomial regret bound without accessing a generative model or making strong assumptions such as ergodicity of the MDP. By constructing a special class of MDPs, we also show that for any algorithms, the regret is lower bounded by Ω(d√T/(1−γ)1.5). Our upper and lower bound results together suggest that the proposed reinforcement learning algorithm is near-optimal up to a (1−γ)−0.5 factor.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-zhou21a, title = {Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping}, author = {Zhou, Dongruo and He, Jiafan and Gu, Quanquan}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {12793--12802}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/zhou21a/zhou21a.pdf}, url = {https://proceedings.mlr.press/v139/zhou21a.html}, abstract = {Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low dimensional space. In this paper, we study reinforcement learning for discounted Markov Decision Processes (MDPs), where the transition kernel can be parameterized as a linear function of certain feature mapping. We propose a novel algorithm which makes use of the feature mapping and obtains a $\tilde O(d\sqrt{T}/(1-\gamma)^2)$ regret, where $d$ is the dimension of the feature space, $T$ is the time horizon and $\gamma$ is the discount factor of the MDP. To the best of our knowledge, this is the first polynomial regret bound without accessing a generative model or making strong assumptions such as ergodicity of the MDP. By constructing a special class of MDPs, we also show that for any algorithms, the regret is lower bounded by $\Omega(d\sqrt{T}/(1-\gamma)^{1.5})$. Our upper and lower bound results together suggest that the proposed reinforcement learning algorithm is near-optimal up to a $(1-\gamma)^{-0.5}$ factor.} }
Endnote
%0 Conference Paper %T Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping %A Dongruo Zhou %A Jiafan He %A Quanquan Gu %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-zhou21a %I PMLR %P 12793--12802 %U https://proceedings.mlr.press/v139/zhou21a.html %V 139 %X Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low dimensional space. In this paper, we study reinforcement learning for discounted Markov Decision Processes (MDPs), where the transition kernel can be parameterized as a linear function of certain feature mapping. We propose a novel algorithm which makes use of the feature mapping and obtains a $\tilde O(d\sqrt{T}/(1-\gamma)^2)$ regret, where $d$ is the dimension of the feature space, $T$ is the time horizon and $\gamma$ is the discount factor of the MDP. To the best of our knowledge, this is the first polynomial regret bound without accessing a generative model or making strong assumptions such as ergodicity of the MDP. By constructing a special class of MDPs, we also show that for any algorithms, the regret is lower bounded by $\Omega(d\sqrt{T}/(1-\gamma)^{1.5})$. Our upper and lower bound results together suggest that the proposed reinforcement learning algorithm is near-optimal up to a $(1-\gamma)^{-0.5}$ factor.
APA
Zhou, D., He, J. & Gu, Q.. (2021). Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:12793-12802 Available from https://proceedings.mlr.press/v139/zhou21a.html.

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