Timezone: »

Finite-Time Last-Iterate Convergence for Multi-Agent Learning in Games
Darren Lin · Zhengyuan Zhou · Panayotis Mertikopoulos · Michael Jordan

Wed Jul 15 05:00 AM -- 05:45 AM & Wed Jul 15 04:00 PM -- 04:45 PM (PDT) @ None #None
In this paper, we consider multi-agent learning via online gradient descent in a class of games called $\lambda$-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 last-iterate convergence rate for joint OGD learning on $\lambda$-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 $\lambda$) and show, via a novel double-stopping time technique, that this adaptive algorithm achieves same finite-time last-iterate convergence rate as non-adaptive 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.

Author Information

Darren Lin (UC Berkeley)
Zhengyuan Zhou (Stanford University)
Panayotis Mertikopoulos (CNRS and Criteo AI Lab)
Michael Jordan (UC Berkeley)

More from the Same Authors