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arXiv · 2304.00771

Continuous-time Analysis of Anchor Acceleration

Jaewook J. Suh·Jisun Park·Ernest K. Ryu
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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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Jaewook J. Suh, Jisun Park, Ernest K. Ryu. 2023-04-03. Continuous-time Analysis of Anchor Acceleration. https://arxiv.org/abs/2304.00771

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