Finite-time last-iterate convergence for multi-agent learning in games

Tianyi Lin (1) , Zhengyuan Zhou (2, 3) , Panayotis Mertikopoulos (4, 5) , Michael I Jordan (1)

1 Berkeley EECS - Department of Electrical Engineering and Computer Sciences
2 NYU - New York University [New York]
3 IBM Watson Research Center
4 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
5 Criteo AI Lab

In this paper, we consider multi-agent learning via online gradient descent in a class of games called λ-cocoercive games, a fairly broad class of games that admits many Nash equilibria and that properly includes unconstrained strongly monotone games. We characterize the finite-time lastiterate convergence rate for joint OGD learning on λ-cocoercive games; further, building on this result, we develop a fully adaptive OGD learning algorithm that does not require any knowledge of problem parameter (e.g. cocoercive constant λ) and show, via a novel double-stopping time technique, that this adaptive algorithm achieves same finite-time last-iterate convergence rate as nonadaptive counterpart. Subsequently, we extend OGD learning to the noisy gradient feedback case and establish last-iterate convergence results-first qualitative almost sure convergence, then quantitative finite-time convergence rates-all under non-decreasing step-sizes. To our knowledge, we provide the first set of results that fill in several gaps of the existing multi-agent online learning literature, where three aspects-finite-time convergence rates, non-decreasing step-sizes, and fully adaptive algorithms have been unexplored before.

Domaines: Optimisation et contrôle [math.OC]

Tianyi Lin, Zhengyuan Zhou, Panayotis Mertikopoulos, Michael I Jordan. Finite-time last-iterate convergence for multi-agent learning in games. ICML 2020 - 37th International Conference on Machine Learning, Jul 2020, Vienna, Austria. pp.1-11. ⟨hal-03043711⟩