Averaged Heavy-Ball Method

Marina Danilova; Grigory Malinovsky

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arXiv · 2111.05430

Averaged Heavy-Ball Method

Marina Danilova·Grigory Malinovsky

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Abstract

Heavy-Ball method (HB) is known for its simplicity in implementation and practical efficiency. However, as with other momentum methods, it has non-monotone behavior, and for optimal parameters, the method suffers from the so-called peak effect. To address this issue, in this paper, we consider an averaged version of Heavy-Ball method (AHB). We show that for quadratic problems AHB has a smaller maximal deviation from the solution than HB. Moreover, for general convex and strongly convex functions, we prove non-accelerated rates of global convergence of AHB and its weighted version. We conduct several numerical experiments on minimizing quadratic and non-quadratic functions to demonstrate the advantages of using averaging for HB.

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Marina Danilova, Grigory Malinovsky. 2021-11-09. Averaged Heavy-Ball Method. https://arxiv.org/abs/2111.05430

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