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Continuous-time Analysis of Anchor Acceleration

Jaewook Suh · Jisun Park · Ernest Ryu

Great Hall & Hall B1+B2 (level 1) #1114
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[ Paper [ Poster [ OpenReview
Thu 14 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: Recently, the anchor acceleration, an acceleration mechanism distinct from Nesterov's, has been discovered for minimax optimization and fixed-point problems, but its mechanism is not understood well, much less so than Nesterov acceleration. In this work, we analyze continuous-time models of anchor acceleration. We provide tight, unified analyses for characterizing the convergence rate as a function of the anchor coefficient $\beta(t)$, thereby providing insight into the anchor acceleration mechanism and its accelerated $\mathcal{O}(1/k^2)$-convergence rate. Finally, we present an adaptive method inspired by the continuous-time analyses and establish its effectiveness through theoretical analyses and experiments.

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