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We explore the use of policy approximations to reduce the computational costof learning Nash equilibria in zero-sum stochastic games. We propose a newQ-learning type algorithm that uses a sequence of entropy-regularized softpolicies to approximate the Nash policy during the Q-function updates. We provethat under certain conditions, by updating the regularized Q-function, thealgorithm converges to a Nash equilibrium. We also demonstrate the proposedalgorithm's ability to transfer previous training experiences, enabling theagents to adapt quickly to new environments. We provide a dynamichyper-parameter scheduling scheme to further expedite convergence. Empiricalresults applied to a number of stochastic games verify that the proposedalgorithm converges to the Nash equilibrium, while exhibiting a major speed-upover existing algorithms.

Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximation