Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback.

The article focuses on developing a novel bandit learning algorithm for no-regret online learning in smooth and strongly monotone games, where players only observe their own rewards (bandit feedback) rather than gradients. Leveraging self-concordant barrier functions within a mirror descent framework, the proposed algorithm achieves both minimax-optimal single-agent regret of order \(\tilde{O}(n\sqrt{T})\) and an optimal last-iterate convergence rate to the unique Nash equilibrium of order \(\tilde{O}(n T^{-1/2})\) in multiagent settings, improving upon prior results. The work rigorously establishes these theoretical guarantees, demonstrates applicability to economic and auction models such as Cournot competition and Kelly auctions, and provides numerical experiments showing faster convergence compared to existing methods. This contribution settles an open problem in bandit game-theoretical learning by presenting the first doubly optimal algorithm that attains optimal regret and convergence rates under bandit feedback in strongly monotone games.