OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression

TL;DR

OpReg-Boost introduces a novel operator regression-based regularization method that accelerates online optimization algorithms, improving convergence rates and reducing errors for time-varying convex problems.

Contribution

The paper proposes OpReg-Boost, a new regularization approach utilizing operator regression to enhance convergence speed of online algorithms for convex optimization.

Findings

OpReg-Boost outperforms classical algorithms like FISTA and Anderson acceleration.

The method achieves linear convergence with reduced asymptotic error.

A computationally-efficient solver based on QCQPs is developed.

Abstract

This paper presents a new regularization approach -- termed OpReg-Boost -- to boost the convergence and lessen the asymptotic error of online optimization and learning algorithms. In particular, the paper considers online algorithms for optimization problems with a time-varying (weakly) convex composite cost. For a given online algorithm, OpReg-Boost learns the closest algorithmic map that yields linear convergence; to this end, the learning procedure hinges on the concept of operator regression. We show how to formalize the operator regression problem and propose a computationally-efficient Peaceman-Rachford solver that exploits a closed-form solution of simple quadratically-constrained quadratic programs (QCQPs). Simulation results showcase the superior properties of OpReg-Boost w.r.t. the more classical forward-backward algorithm, FISTA, and Anderson acceleration.