Backtracking strategies for accelerated descent methods with smooth composite objectives

TL;DR

This paper introduces a backtracking strategy for accelerated descent methods with smooth composite objectives, allowing adaptive step size adjustments and proving faster convergence, with applications demonstrated in imaging problems.

Contribution

It proposes a novel backtracking rule for Fast Iterative Shrinkage/Thresholding Algorithms that adaptively adjusts step sizes, improving convergence rates over classical methods.

Findings

Accelerated convergence rates are theoretically proven.

Numerical experiments show improved performance in imaging tasks.

The method allows local step size adjustments, enhancing flexibility.

Abstract

We present and analyse a backtracking strategy for a general Fast Iterative Shrinkage/Thresholding Algorithm which has been recently proposed in (Chambolle, Pock, 2016) for strongly convex objective functions. Differently from classical Armijo-type line searching, our backtracking rule allows for local increasing and decreasing of the descent step size (i.e. proximal parameter) along the iterations. For such strategy accelerated convergence rates are proved and numerical results are shown for some exemplar imaging problems.