Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity

Aaron Sidford, Mengdi Wang, Lin Yang, Yinyu Ye
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2992-3002, 2020.

Abstract

In this paper we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that computes an $\epsilon$-optimal strategy with high-probability given $\tilde{O}((1 - \gamma)^{-3} \epsilon^{-2})$ samples from the transition function for each state-action-pair. Our algorithm runs in time nearly linear in the number of samples and uses space nearly linear in the number of state-action pairs. As stochastic games generalize Markov decision processes (MDPs) our runtime and sample complexities are optimal due to \cite{azar2013minimax}. We achieve our results by showing how to generalize a near-optimal Q-learning based algorithms for MDP, in particular \cite{sidford2018near}, to two-player strategy computation algorithms. This overcomes limitations of standard Q-learning and strategy iteration or alternating minimization based approaches and we hope will pave the way for future reinforcement learning results by facilitating the extension of MDP results to multi-agent settings with little loss.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-sidford20a, title = {Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity}, author = {Sidford, Aaron and Wang, Mengdi and Yang, Lin and Ye, Yinyu}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2992--3002}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/sidford20a/sidford20a.pdf}, url = {https://proceedings.mlr.press/v108/sidford20a.html}, abstract = {In this paper we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that computes an $\epsilon$-optimal strategy with high-probability given $\tilde{O}((1 - \gamma)^{-3} \epsilon^{-2})$ samples from the transition function for each state-action-pair. Our algorithm runs in time nearly linear in the number of samples and uses space nearly linear in the number of state-action pairs. As stochastic games generalize Markov decision processes (MDPs) our runtime and sample complexities are optimal due to \cite{azar2013minimax}. We achieve our results by showing how to generalize a near-optimal Q-learning based algorithms for MDP, in particular \cite{sidford2018near}, to two-player strategy computation algorithms. This overcomes limitations of standard Q-learning and strategy iteration or alternating minimization based approaches and we hope will pave the way for future reinforcement learning results by facilitating the extension of MDP results to multi-agent settings with little loss.} }
Endnote
%0 Conference Paper %T Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity %A Aaron Sidford %A Mengdi Wang %A Lin Yang %A Yinyu Ye %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-sidford20a %I PMLR %P 2992--3002 %U https://proceedings.mlr.press/v108/sidford20a.html %V 108 %X In this paper we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that computes an $\epsilon$-optimal strategy with high-probability given $\tilde{O}((1 - \gamma)^{-3} \epsilon^{-2})$ samples from the transition function for each state-action-pair. Our algorithm runs in time nearly linear in the number of samples and uses space nearly linear in the number of state-action pairs. As stochastic games generalize Markov decision processes (MDPs) our runtime and sample complexities are optimal due to \cite{azar2013minimax}. We achieve our results by showing how to generalize a near-optimal Q-learning based algorithms for MDP, in particular \cite{sidford2018near}, to two-player strategy computation algorithms. This overcomes limitations of standard Q-learning and strategy iteration or alternating minimization based approaches and we hope will pave the way for future reinforcement learning results by facilitating the extension of MDP results to multi-agent settings with little loss.
APA
Sidford, A., Wang, M., Yang, L. & Ye, Y.. (2020). Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2992-3002 Available from https://proceedings.mlr.press/v108/sidford20a.html.

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