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This paper proves that a common no-regret learning algorithm, optimistic FTRL, converges linearly to Nash equilibrium in a class of multiplayer games, under mild conditions and for several regularizers. The work is theoretical and targets multi-agent learning dynamics rather than deployed systems, so its practical reach depends on whether these guarantees extend beyond harmonic games. For ML readers, the useful takeaway is the energy-function analysis of dual iterates, which may inform convergence proofs for other learning algorithms in competitive settings.
Linear Last-Iterate Convergence Rates for Optimistic Learning in Harmonic Games
arXiv:2610.18560v1 Announce Type: cross Abstract: We prove that the last iterate of Optimistic Follow-The-Regularized-Leader (OFTRL) converges at a linear rate to a Nash equilibrium in multiplayer harmonic games. Our result holds under a mild game-regularity condition and for a large family of regularizers, including entropy, Tsallis, and log-barrier. Our analysis is based on a dual perspective of OFTRL: we prove that the interaction between optimism and the global structure of harmonic games leads to the dissipation of an energy function along the dual iterates, for which we establish tight quantitative bounds. Our result also holds for the Extragradient FTRL variant.
Abstract:We prove that the last iterate of Optimistic Follow-The-Regularized-Leader (OFTRL) converges at a linear rate to a Nash equilibrium in multiplayer harmonic games. Our result holds under a mild game-regularity condition and for a large family of regularizers, including entropy, Tsallis, and log-barrier. Our analysis is based on a dual perspective of OFTRL: we prove that the interaction between optimism and the global structure of harmonic games leads to the dissipation of an energy function along the dual iterates, for which we establish tight quantitative bounds. Our result also holds for the Extragradient FTRL variant.
Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG)
arXiv:2610.18560 [cs.GT]
(or arXiv:2610.18560v1 [cs.GT] for this version)
https://doi.org/10.48550/arXiv.2610.18560 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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