\(\varepsilon\)-Optimally Solving Two-Player Zero-Sum POSGs

Abstract

We present a novel framework for \(\varepsilon\)-optimally solving two-player zero-sum partially observable stochastic games (zs-POSGs). These games pose a major challenge due to the absence of a principled connection with dynamic programming (DP) techniques developed for two-player zero-sum stochastic games (zs-SGs). Prior attempts at transferring solution methods have lacked a lossless reduction—defined here as a transformation that preserves value functions, equilibrium strategies, and optimality structure—thereby limiting generalisation to ad hoc algorithms. This work introduces the first lossless reduction from zs-POSGs to transition-independent zs-SGs, enabling the principled application of a broad class of DP-based methods. We show empirically that point-based value iteration (PBVI) algorithms, applied via this reduction, produce \(\varepsilon\)-optimal strategies across a range of benchmark domains, consistently matching or outperforming existing state-of-the-art methods. Our results open a systematic pathway for algorithmic and theoretical transfer from SGs to partially observable settings.