Continuous-time Analysis of Anchor Acceleration

Jaewook J. Suh, Jisun Park, Ernest K. Ryu

Keywords: acceleration, convex optimization, continuous-time analysis, monotone operator, monotone inclusion, minimax optimization, fixed-point problem, anchor acceleration

TL;DR: We present continuous-time analyses of anchor acceleration for minimax optimization and monotone inclusion problems.

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.

Submission Number: 3067