Deep SOR Minimax Q-learning for Two-player Zero-sum Game

Saksham Gautam; Lakshmi Mandal; Shalabh Bhatnagar

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arXiv · 2511.16226

Deep SOR Minimax Q-learning for Two-player Zero-sum Game

Saksham Gautam·Lakshmi Mandal·Shalabh Bhatnagar

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Abstract

In this work, we consider the problem of a two-player zero-sum game. In the literature, the successive over-relaxation Q-learning algorithm has been developed and implemented, and it is seen to result in a lower contraction factor for the associated Q-Bellman operator resulting in a faster value iteration-based procedure. However, this has been presented only for the tabular case and not for the setting with function approximation that typically caters to real-world high-dimensional state-action spaces. Furthermore, such settings in the case of two-player zero-sum games have not been considered. We thus propose a deep successive over-relaxation minimax Q-learning algorithm that incorporates deep neural networks as function approximators and is suitable for high-dimensional spaces. We prove the finite-time convergence of the proposed algorithm. Through numerical experiments, we show the effectiveness of the proposed method over the existing Q-learning algorithm. Our ablation studies demonstrate the effect of different values of the crucial successive over-relaxation parameter.

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BibTeX RIS

Saksham Gautam, Lakshmi Mandal, Shalabh Bhatnagar. 2025-11-20. Deep SOR Minimax Q-learning for Two-player Zero-sum Game. https://arxiv.org/abs/2511.16226

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