Minimax Last-Iterate Convergence in Matrix Games with Observed Actions

Yuheng Zhang

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arXiv · 2609.34656

Minimax Last-Iterate Convergence in Matrix Games with Observed Actions

Yuheng Zhang

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Abstract

We study last-iterate convergence in unknown two-player zero-sum matrix games with bandit payoff feedback and observed opponent actions. For games with $d$ actions per player, we develop an algorithm achieving a duality gap of $\widetilde{\mathcal{O}}(\sqrt{d/t})$ with high probability, simultaneously at every round $t$. This improves the dimension dependence of the best previously known guarantee by a factor of $d^{3/2}$. The rate matches a standard bandit lower bound, establishing minimax optimality in both the number of actions and the number of rounds, up to logarithmic factors. The algorithm is computationally efficient, requiring only $\mathcal{O}(d)$ time and memory per round. Our technical contribution is a joint design of adaptive averaging and corrected exponential weights that absorbs estimation variance, together with a potential argument that bounds phase durations.

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Yuheng Zhang. 2026-09-28. Minimax Last-Iterate Convergence in Matrix Games with Observed Actions. https://arxiv.org/abs/2609.34656

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