Provably Efficient Generalized Lagrangian Policy Optimization for Safe Multi-Agent Reinforcement Learning

Dongsheng Ding, Xiaohan Wei, Zhuoran Yang, Zhaoran Wang, Mihailo Jovanovic
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:315-332, 2023.

Abstract

We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic two-player zero-sum constrained Markov game with independent transition functions that are unknown to agents, adversarial reward functions, and stochastic utility functions. For such a Markov game, we employ an approach based on the occupancy measure to formulate it as an online constrained saddle-point problem with an explicit constraint. We extend the Lagrange multiplier method in constrained optimization to handle the constraint by creating a generalized Lagrangian with minimax decision primal variables and a dual variable. Next, we develop an upper confidence reinforcement learning algorithm to solve this Lagrangian problem while balancing exploration and exploitation. Our algorithm updates the minimax decision primal variables via online mirror descent and the dual variable via projected gradient step and we prove that it enjoys sublinear rate $ O((|X|+|Y|) L \sqrt{T(|A|+|B|)}))$ for both regret and constraint violation after playing $T$ episodes of the game. Here, $L$ is the horizon of each episode, $(|X|,|A|)$ and $(|Y|,|B|)$ are the state/action space sizes of the min-player and the max-player, respectively. To the best of our knowledge, we provide the first provably efficient online safe reinforcement learning algorithm in constrained Markov games.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-ding23a, title = {Provably Efficient Generalized Lagrangian Policy Optimization for Safe Multi-Agent Reinforcement Learning}, author = {Ding, Dongsheng and Wei, Xiaohan and Yang, Zhuoran and Wang, Zhaoran and Jovanovic, Mihailo}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {315--332}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/ding23a/ding23a.pdf}, url = {https://proceedings.mlr.press/v211/ding23a.html}, abstract = {We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic two-player zero-sum constrained Markov game with independent transition functions that are unknown to agents, adversarial reward functions, and stochastic utility functions. For such a Markov game, we employ an approach based on the occupancy measure to formulate it as an online constrained saddle-point problem with an explicit constraint. We extend the Lagrange multiplier method in constrained optimization to handle the constraint by creating a generalized Lagrangian with minimax decision primal variables and a dual variable. Next, we develop an upper confidence reinforcement learning algorithm to solve this Lagrangian problem while balancing exploration and exploitation. Our algorithm updates the minimax decision primal variables via online mirror descent and the dual variable via projected gradient step and we prove that it enjoys sublinear rate $ O((|X|+|Y|) L \sqrt{T(|A|+|B|)}))$ for both regret and constraint violation after playing $T$ episodes of the game. Here, $L$ is the horizon of each episode, $(|X|,|A|)$ and $(|Y|,|B|)$ are the state/action space sizes of the min-player and the max-player, respectively. To the best of our knowledge, we provide the first provably efficient online safe reinforcement learning algorithm in constrained Markov games.} }
Endnote
%0 Conference Paper %T Provably Efficient Generalized Lagrangian Policy Optimization for Safe Multi-Agent Reinforcement Learning %A Dongsheng Ding %A Xiaohan Wei %A Zhuoran Yang %A Zhaoran Wang %A Mihailo Jovanovic %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-ding23a %I PMLR %P 315--332 %U https://proceedings.mlr.press/v211/ding23a.html %V 211 %X We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic two-player zero-sum constrained Markov game with independent transition functions that are unknown to agents, adversarial reward functions, and stochastic utility functions. For such a Markov game, we employ an approach based on the occupancy measure to formulate it as an online constrained saddle-point problem with an explicit constraint. We extend the Lagrange multiplier method in constrained optimization to handle the constraint by creating a generalized Lagrangian with minimax decision primal variables and a dual variable. Next, we develop an upper confidence reinforcement learning algorithm to solve this Lagrangian problem while balancing exploration and exploitation. Our algorithm updates the minimax decision primal variables via online mirror descent and the dual variable via projected gradient step and we prove that it enjoys sublinear rate $ O((|X|+|Y|) L \sqrt{T(|A|+|B|)}))$ for both regret and constraint violation after playing $T$ episodes of the game. Here, $L$ is the horizon of each episode, $(|X|,|A|)$ and $(|Y|,|B|)$ are the state/action space sizes of the min-player and the max-player, respectively. To the best of our knowledge, we provide the first provably efficient online safe reinforcement learning algorithm in constrained Markov games.
APA
Ding, D., Wei, X., Yang, Z., Wang, Z. & Jovanovic, M.. (2023). Provably Efficient Generalized Lagrangian Policy Optimization for Safe Multi-Agent Reinforcement Learning. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:315-332 Available from https://proceedings.mlr.press/v211/ding23a.html.

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