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Conference Papers Year : 2020

Complexity Guarantees for Polyak Steps with Momentum

Abstract

In smooth strongly convex optimization, or in the presence of H\"olderian error bounds, knowledge of the curvature parameter is critical for obtaining simple methods with accelerated rates. In this work, we study a class of methods, based on Polyak steps, where this knowledge is substituted by that of the optimal value, $f_*$. We first show slightly improved convergence bounds than previously known for the classical case of simple gradient descent with Polyak steps, we then derive an accelerated gradient method with Polyak steps and momentum, along with convergence guarantees.

Dates and versions

hal-02470997 , version 1 (07-02-2020)

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Cite

Mathieu Barré, Adrien Taylor, Alexandre d'Aspremont. Complexity Guarantees for Polyak Steps with Momentum. COLT 2020 - 33rd Annual Conference on Learning Theory, Jul 2020, Graz / Virtual, Austria. ⟨hal-02470997⟩
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