Boosting Perturbed Gradient Ascent for Last-Iterate Convergence in Games

Kenshi Abe, Mitsuki Sakamoto, Kaito Ariu, Atsushi Iwasaki

Keywords: Last-Iterate Convergence, Learning in Games, Noisy Feedback

TL;DR: This paper proposes a novel payoff-perturbed Gradient Ascent that achieves fast last-iterate convergence rates.

Abstract: This paper introduces 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 an anchoring or reference strategy, which is periodically re-initialized. In response, this paper proposes 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.

Primary Area: Algorithmic game theory

Submission Number: 17156