Optimal last-iterate convergence in matrix games with bandit feedback using the log-barrier
Provides the first algorithm to attain the optimal convergence rate for uncoupled players in zero-sum matrix games with bandit feedback, solving an open problem.
The paper achieves optimal last-iterate convergence rate of Õ(t^{-1/4}) in zero-sum matrix games with bandit feedback, matching the lower bound, and extends this result to extensive-form games.
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.