Optimal last-iterate convergence in matrix games with bandit feedback using the log-barrier
arXiv cs.LG / 4/17/2026
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Key Points
- The paper studies how to learn minimax policies in zero-sum matrix games under bandit-style feedback, focusing on achieving last-iterate convergence.
- Prior work (Fiegel et al., 2025) showed that when players are uncoupled, last-iterate convergence is fundamentally harder, with a lower bound of order Ω(t^{-1/4}) on the exploitability gap.
- The authors propose online mirror descent with log-barrier regularization and a dual-focused analysis, proving a high-probability convergence rate of O~(t^{-1/4}) (up to log factors).
- They further extend the approach to extensive-form games, obtaining a similar O~(t^{-1/4}) rate for last-iterate convergence.
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