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arXiv · 2604.15242

Optimal last-iterate convergence in matrix games with bandit feedback using the log-barrier

Come Fiegel·Pierre Menard·Tadashi Kozuno·Michal Valko·Vianney Perchet
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Abstract

We study the problem of learning minimax policies in zero-sum matrix games. Fiegel et al. (2025) recently showed that achieving last-iterate convergence in this setting is harder when the players are uncoupled, by proving a lower bound on the exploitability gap of Omega(t^{-1/4}). Some online mirror descent algorithms were proposed in the literature for this problem, but none have truly attained this rate yet. We show that the use of a log-barrier regularization, along with a dual-focused analysis, allows this O-tilde(t^{-1/4}) convergence with high-probability. We additionally extend our idea to the setting of extensive-form games, proving a bound with the same rate.

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Come Fiegel, Pierre Menard, Tadashi Kozuno, Michal Valko, Vianney Perchet. 2026-04-16. Optimal last-iterate convergence in matrix games with bandit feedback using the log-barrier. https://arxiv.org/abs/2604.15242

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