Solving Discounted Stochastic TwoPlayer Games with NearOptimal Time and Sample Complexity
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:29923002, 2020.
Abstract
In this paper we settle the sampling complexity of solving discounted twoplayer turnbased zerosum 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 highprobability given $\tilde{O}((1  \gamma)^{3} \epsilon^{2})$ samples from the transition function for each stateactionpair. Our algorithm runs in time nearly linear in the number of samples and uses space nearly linear in the number of stateaction 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 nearoptimal Qlearning based algorithms for MDP, in particular \cite{sidford2018near}, to twoplayer strategy computation algorithms. This overcomes limitations of standard Qlearning 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 multiagent settings with little loss.
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