Reward-Mixing MDPs with Few Latent Contexts are Learnable

Jeongyeol Kwon, Yonathan Efroni, Constantine Caramanis, Shie Mannor
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:18057-18082, 2023.

Abstract

We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs): at the beginning of every episode nature randomly picks a latent reward model among $M$ candidates and an agent interacts with the MDP throughout the episode for $H$ time steps. Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model. Prior work established an upper bound for RMMDPs with $M=2$. In this work, we resolve several open questions for the general RMMDP setting. We consider an arbitrary $M\ge2$ and provide a sample-efficient algorithm–$EM^2$–that outputs an $\epsilon$-optimal policy using $O \left(\epsilon^{-2} \cdot S^d A^d \cdot \text{poly}(H, Z)^d \right)$ episodes, where $S, A$ are the number of states and actions respectively, $H$ is the time-horizon, $Z$ is the support size of reward distributions and $d=O(\min(M,H))$. We also provide a $(SA)^{\Omega(\sqrt{M})} / \epsilon^{2}$ lower bound, supporting that super-polynomial sample complexity in $M$ is necessary.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-kwon23b, title = {Reward-Mixing {MDP}s with Few Latent Contexts are Learnable}, author = {Kwon, Jeongyeol and Efroni, Yonathan and Caramanis, Constantine and Mannor, Shie}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {18057--18082}, 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/kwon23b/kwon23b.pdf}, url = {https://proceedings.mlr.press/v202/kwon23b.html}, abstract = {We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs): at the beginning of every episode nature randomly picks a latent reward model among $M$ candidates and an agent interacts with the MDP throughout the episode for $H$ time steps. Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model. Prior work established an upper bound for RMMDPs with $M=2$. In this work, we resolve several open questions for the general RMMDP setting. We consider an arbitrary $M\ge2$ and provide a sample-efficient algorithm–$EM^2$–that outputs an $\epsilon$-optimal policy using $O \left(\epsilon^{-2} \cdot S^d A^d \cdot \text{poly}(H, Z)^d \right)$ episodes, where $S, A$ are the number of states and actions respectively, $H$ is the time-horizon, $Z$ is the support size of reward distributions and $d=O(\min(M,H))$. We also provide a $(SA)^{\Omega(\sqrt{M})} / \epsilon^{2}$ lower bound, supporting that super-polynomial sample complexity in $M$ is necessary.} }
Endnote
%0 Conference Paper %T Reward-Mixing MDPs with Few Latent Contexts are Learnable %A Jeongyeol Kwon %A Yonathan Efroni %A Constantine Caramanis %A Shie Mannor %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-kwon23b %I PMLR %P 18057--18082 %U https://proceedings.mlr.press/v202/kwon23b.html %V 202 %X We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs): at the beginning of every episode nature randomly picks a latent reward model among $M$ candidates and an agent interacts with the MDP throughout the episode for $H$ time steps. Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model. Prior work established an upper bound for RMMDPs with $M=2$. In this work, we resolve several open questions for the general RMMDP setting. We consider an arbitrary $M\ge2$ and provide a sample-efficient algorithm–$EM^2$–that outputs an $\epsilon$-optimal policy using $O \left(\epsilon^{-2} \cdot S^d A^d \cdot \text{poly}(H, Z)^d \right)$ episodes, where $S, A$ are the number of states and actions respectively, $H$ is the time-horizon, $Z$ is the support size of reward distributions and $d=O(\min(M,H))$. We also provide a $(SA)^{\Omega(\sqrt{M})} / \epsilon^{2}$ lower bound, supporting that super-polynomial sample complexity in $M$ is necessary.
APA
Kwon, J., Efroni, Y., Caramanis, C. & Mannor, S.. (2023). Reward-Mixing MDPs with Few Latent Contexts are Learnable. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:18057-18082 Available from https://proceedings.mlr.press/v202/kwon23b.html.

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