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Title: Tight last-iterate convergence rates for no-regret learning in multi-player games.
https://arxiv.org/abs/2010.13724 We study the question of obtaining last-iterate convergence rates for no-regret learning algorithms in multi-player games. We show that the optimistic gradient (OG) algorithm with a constant step-size, which is no-regret, achieves a last-iterate rate of O(1/T‾‾√) with respect to the gap function in smooth monotone games. This result addresses a question of Mertikopoulos & Zhou (2018), who asked whether extra-gradient approaches (such as OG) can be applied to achieve improved guarantees in the multi-agent learning setting. The proof of our upper bound uses a new technique centered around an adaptive choice of potential function at each iteration. We also show that the O(1/T‾‾√) rate is tight for all p-SCLI algorithms, which includes OG as a special case. As a byproduct of our lower bound analysis we additionally present a proof of a conjecture of Arjevani et al. (2015) which is more direct than previous approaches.  more » « less
Award ID(s):
1741137
NSF-PAR ID:
10228237
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
34th Annual Conference on Neural Information Processing Systems (NeurIPS), NeurIPS 2020
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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