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arXiv · 2112.06181

On the Heterogeneity of Independent Learning Dynamics in Zero-sum Stochastic Games

Muhammed O. Sayin·K. Alperen Cetiner
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Abstract

We analyze the convergence properties of the two-timescale fictitious play combining the classical fictitious play with the Q-learning for two-player zero-sum stochastic games with player-dependent learning rates. We show its almost sure convergence under the standard assumptions in two-timescale stochastic approximation methods when the discount factor is less than the product of the ratios of player-dependent step sizes. To this end, we formulate a novel Lyapunov function formulation and present a one-sided asynchronous convergence result.

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Muhammed O. Sayin, K. Alperen Cetiner. 2021-12-12. On the Heterogeneity of Independent Learning Dynamics in Zero-sum Stochastic Games. https://arxiv.org/abs/2112.06181

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