Provably Efficient Safe Exploration via Primal-Dual Policy Optimization

Dongsheng Ding, Xiaohan Wei, Zhuoran Yang, Zhaoran Wang, Mihailo Jovanovic
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3304-3312, 2021.

Abstract

We study the safe reinforcement learning problem using the constrained Markov decision processes in which an agent aims to maximize the expected total reward subject to a safety constraint on the expected total value of a utility function. We focus on an episodic setting with the function approximation where the Markov transition kernels have a linear structure but do not impose any additional assumptions on the sampling model. Designing safe reinforcement learning algorithms with provable computational and statistical efficiency is particularly challenging under this setting because of the need to incorporate both the safety constraint and the function approximation into the fundamental exploitation/exploration tradeoff. To this end, we present an \underline{O}ptimistic \underline{P}rimal-\underline{D}ual Proximal Policy \underline{OP}timization \mbox{(OPDOP)} algorithm where the value function is estimated by combining the least-squares policy evaluation and an additional bonus term for safe exploration. We prove that the proposed algorithm achieves an $\tilde{O}(d H^{2.5}\sqrt{T})$ regret and an $\tilde{O}(d H^{2.5}\sqrt{T})$ constraint violation, where $d$ is the dimension of the feature mapping, $H$ is the horizon of each episode, and $T$ is the total number of steps. These bounds hold when the reward/utility functions are fixed but the feedback after each episode is bandit. Our bounds depend on the capacity of the state-action space only through the dimension of the feature mapping and thus our results hold even when the number of states goes to infinity. To the best of our knowledge, we provide the first provably efficient online policy optimization algorithm for constrained Markov decision processes in the function approximation setting, with safe exploration.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-ding21d, title = { Provably Efficient Safe Exploration via Primal-Dual Policy Optimization }, author = {Ding, Dongsheng and Wei, Xiaohan and Yang, Zhuoran and Wang, Zhaoran and Jovanovic, Mihailo}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3304--3312}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/ding21d/ding21d.pdf}, url = {https://proceedings.mlr.press/v130/ding21d.html}, abstract = { We study the safe reinforcement learning problem using the constrained Markov decision processes in which an agent aims to maximize the expected total reward subject to a safety constraint on the expected total value of a utility function. We focus on an episodic setting with the function approximation where the Markov transition kernels have a linear structure but do not impose any additional assumptions on the sampling model. Designing safe reinforcement learning algorithms with provable computational and statistical efficiency is particularly challenging under this setting because of the need to incorporate both the safety constraint and the function approximation into the fundamental exploitation/exploration tradeoff. To this end, we present an \underline{O}ptimistic \underline{P}rimal-\underline{D}ual Proximal Policy \underline{OP}timization \mbox{(OPDOP)} algorithm where the value function is estimated by combining the least-squares policy evaluation and an additional bonus term for safe exploration. We prove that the proposed algorithm achieves an $\tilde{O}(d H^{2.5}\sqrt{T})$ regret and an $\tilde{O}(d H^{2.5}\sqrt{T})$ constraint violation, where $d$ is the dimension of the feature mapping, $H$ is the horizon of each episode, and $T$ is the total number of steps. These bounds hold when the reward/utility functions are fixed but the feedback after each episode is bandit. Our bounds depend on the capacity of the state-action space only through the dimension of the feature mapping and thus our results hold even when the number of states goes to infinity. To the best of our knowledge, we provide the first provably efficient online policy optimization algorithm for constrained Markov decision processes in the function approximation setting, with safe exploration. } }
Endnote
%0 Conference Paper %T Provably Efficient Safe Exploration via Primal-Dual Policy Optimization %A Dongsheng Ding %A Xiaohan Wei %A Zhuoran Yang %A Zhaoran Wang %A Mihailo Jovanovic %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-ding21d %I PMLR %P 3304--3312 %U https://proceedings.mlr.press/v130/ding21d.html %V 130 %X We study the safe reinforcement learning problem using the constrained Markov decision processes in which an agent aims to maximize the expected total reward subject to a safety constraint on the expected total value of a utility function. We focus on an episodic setting with the function approximation where the Markov transition kernels have a linear structure but do not impose any additional assumptions on the sampling model. Designing safe reinforcement learning algorithms with provable computational and statistical efficiency is particularly challenging under this setting because of the need to incorporate both the safety constraint and the function approximation into the fundamental exploitation/exploration tradeoff. To this end, we present an \underline{O}ptimistic \underline{P}rimal-\underline{D}ual Proximal Policy \underline{OP}timization \mbox{(OPDOP)} algorithm where the value function is estimated by combining the least-squares policy evaluation and an additional bonus term for safe exploration. We prove that the proposed algorithm achieves an $\tilde{O}(d H^{2.5}\sqrt{T})$ regret and an $\tilde{O}(d H^{2.5}\sqrt{T})$ constraint violation, where $d$ is the dimension of the feature mapping, $H$ is the horizon of each episode, and $T$ is the total number of steps. These bounds hold when the reward/utility functions are fixed but the feedback after each episode is bandit. Our bounds depend on the capacity of the state-action space only through the dimension of the feature mapping and thus our results hold even when the number of states goes to infinity. To the best of our knowledge, we provide the first provably efficient online policy optimization algorithm for constrained Markov decision processes in the function approximation setting, with safe exploration.
APA
Ding, D., Wei, X., Yang, Z., Wang, Z. & Jovanovic, M.. (2021). Provably Efficient Safe Exploration via Primal-Dual Policy Optimization . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3304-3312 Available from https://proceedings.mlr.press/v130/ding21d.html.

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