Extrapolation-based Prediction-Correction Methods for Time-varying Convex Optimization

TL;DR

This paper introduces extrapolation-based prediction-correction algorithms for online convex optimization, providing convergence analysis and empirical validation in signal processing, machine learning, and robotics.

Contribution

It proposes a novel extrapolation-based prediction strategy tailored for time-varying convex problems, with theoretical convergence guarantees and practical performance assessments.

Findings

Explicit tracking error bounds derived

Algorithms demonstrate effective real-world performance

Convergence analysis applicable to primal and dual problems

Abstract

In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems.