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arXiv · 2110.01030

A Recursive Algorithm for Solving Simple Stochastic Games

Xavier Badin de Montjoye
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Abstract

We present two recursive strategy improvement algorithms for solving simple stochastic games. First we present an algorithm for solving SSGs of degree $d$ that uses at most $O\left(\left\lfloor(d+1)^2/2\right\rfloor^{n/2}\right)$ iterations, with $n$ the number of MAX vertices. Then, we focus on binary SSG and propose an algorithm that has complexity $O\left(\varphi^nPoly(N)\right)$ where $\varphi = (1 + \sqrt{5})/2$ is the golden ratio. To the best of our knowledge, this is the first deterministic strategy improvement algorithm that visits $2^{cn}$ strategies with $c < 1$.

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Xavier Badin de Montjoye. 2021-10-03. A Recursive Algorithm for Solving Simple Stochastic Games. https://arxiv.org/abs/2110.01030

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