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.
Fiegel et al. (Thu,) studied this question.