An Accelerated Composite Gradient Method for Large-scale Composite Objective Problems

TL;DR

This paper introduces the Accelerated Composite Gradient Method (ACGM), a new first-order optimization algorithm designed for large-scale composite problems, offering faster convergence and an efficient step size search.

Contribution

The paper presents a novel accelerated gradient method based on the augmented estimate sequence framework, improving convergence rates for large-scale composite objective problems.

Findings

ACGM outperforms existing methods in convergence speed.

The method is effective for both strongly and non-strongly convex problems.

Simulation results validate the theoretical improvements.

Abstract

We introduce a framework, which we denote as the augmented estimate sequence, for deriving fast algorithms with provable convergence guarantees. We use this framework to construct a new first-order scheme, the Accelerated Composite Gradient Method (ACGM), for large-scale problems with composite objective structure. ACGM surpasses the state-of-the-art methods for this problem class in terms of provable convergence rate, both in the strongly and non-strongly convex cases, and is endowed with an efficient step size search procedure. We support the effectiveness of our new method with simulation results.