Fast Rates for Maximum Entropy Exploration

Daniil Tiapkin, Denis Belomestny, Daniele Calandriello, Eric Moulines, Remi Munos, Alexey Naumov, Pierre Perrault, Yunhao Tang, Michal Valko, Pierre Menard
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:34161-34221, 2023.

Abstract

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al. (2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has $\widetilde{\mathcal{O}}(H^3S^2A/\varepsilon^2)$ sample complexity thus improving the $\varepsilon$-dependence upon existing results, where $S$ is a number of states, $A$ is a number of actions, $H$ is an episode length, and $\varepsilon$ is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order $\widetilde{\mathcal{O}}(\mathrm{poly}(S,A,H)/\varepsilon)$. Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to $\widetilde{\mathcal{O}}(H^2SA/\varepsilon^2)$, yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-tiapkin23a, title = {Fast Rates for Maximum Entropy Exploration}, author = {Tiapkin, Daniil and Belomestny, Denis and Calandriello, Daniele and Moulines, Eric and Munos, Remi and Naumov, Alexey and Perrault, Pierre and Tang, Yunhao and Valko, Michal and Menard, Pierre}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {34161--34221}, 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/tiapkin23a/tiapkin23a.pdf}, url = {https://proceedings.mlr.press/v202/tiapkin23a.html}, abstract = {We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al. (2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has $\widetilde{\mathcal{O}}(H^3S^2A/\varepsilon^2)$ sample complexity thus improving the $\varepsilon$-dependence upon existing results, where $S$ is a number of states, $A$ is a number of actions, $H$ is an episode length, and $\varepsilon$ is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order $\widetilde{\mathcal{O}}(\mathrm{poly}(S,A,H)/\varepsilon)$. Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to $\widetilde{\mathcal{O}}(H^2SA/\varepsilon^2)$, yielding a statistical separation between maximum entropy exploration and reward-free exploration.} }
Endnote
%0 Conference Paper %T Fast Rates for Maximum Entropy Exploration %A Daniil Tiapkin %A Denis Belomestny %A Daniele Calandriello %A Eric Moulines %A Remi Munos %A Alexey Naumov %A Pierre Perrault %A Yunhao Tang %A Michal Valko %A Pierre Menard %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-tiapkin23a %I PMLR %P 34161--34221 %U https://proceedings.mlr.press/v202/tiapkin23a.html %V 202 %X We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al. (2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has $\widetilde{\mathcal{O}}(H^3S^2A/\varepsilon^2)$ sample complexity thus improving the $\varepsilon$-dependence upon existing results, where $S$ is a number of states, $A$ is a number of actions, $H$ is an episode length, and $\varepsilon$ is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order $\widetilde{\mathcal{O}}(\mathrm{poly}(S,A,H)/\varepsilon)$. Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to $\widetilde{\mathcal{O}}(H^2SA/\varepsilon^2)$, yielding a statistical separation between maximum entropy exploration and reward-free exploration.
APA
Tiapkin, D., Belomestny, D., Calandriello, D., Moulines, E., Munos, R., Naumov, A., Perrault, P., Tang, Y., Valko, M. & Menard, P.. (2023). Fast Rates for Maximum Entropy Exploration. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:34161-34221 Available from https://proceedings.mlr.press/v202/tiapkin23a.html.

Related Material