2024/10/03 by Kenshi Abe, Abe, Kenshi, Mitsuki Sakamoto +5 · 1 citation
Computer Science · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Matrix Theory and Algorithms #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2410.02388
openalex publication_date 2024/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a payoff perturbation technique, introducing a strong convexity to players' payoff functions in games. This technique is specifically designed for first-order methods to achieve last-iterate convergence in games where the gradient of the payoff functions is monotone in the strategy profile space, potentially containing additive noise. Although perturbation is known to facilitate the convergence of learning algorithms, the magnitude of perturbation requires careful adjustment to ensure last-iterate convergence. Previous studies have proposed a scheme in which the magnitude is determined by the distance from a periodically re-initialized anchoring or reference strategy. Building upon this, we propose Gradient Ascent with Boosting Payoff Perturbation, which incorporates a novel perturbation into the underlying payoff function, maintaining the periodically re-initializing anchoring strategy scheme. This innovation empowers us to provide faster last-iterate convergence rates against the existing payoff perturbed algorithms, even in the presence of additive noise.