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Non-cooperative games serve as a powerful framework for capturing theinteractions among self-interested players and have broad applicability inmodeling a wide range of practical scenarios, ranging from power management todrug delivery. Although most existing solution algorithms assume theavailability of first-order information or full knowledge of the objectives andothers' action profiles, there are situations where the only accessibleinformation at players' disposal is the realized objective function values. Inthis paper, we devise a bandit online learning algorithm for merely coherentgames that integrates the optimistic mirror descent scheme and multi-pointpseudo-gradient estimates. We further demonstrate that the generated actualsequence of play can converge a.s. to a critical point if the sequences ofquery radius and sample size are chosen properly, without resorting to extraTikhonov regularization terms or additional norm conditions. Finally, weillustrate the validity of the proposed algorithm via a Rock-Paper-Scissorsgame and a least square estimation game.

Bandit Online Learning in Merely Coherent Games with Multi-Point Pseudo-Gradient Estimate