Control-Based Online Distributed Optimization

TL;DR

This paper introduces a control-theoretic approach to develop a fully distributed online optimization algorithm that converges to optimal solutions, demonstrating superior performance over existing methods in various scenarios.

Contribution

The paper presents a novel control-based framework for online distributed optimization, including an algorithm design and internal model acquisition routine, applicable to quadratic and non-quadratic problems.

Findings

Algorithm converges exactly to optimal solutions.

Outperforms alternative algorithms in experiments.

Effective even with inexact internal models.

Abstract

In this paper we design a novel class of online distributed optimization algorithms leveraging control theoretical techniques. We start by focusing on quadratic costs, and assuming to know an internal model of their variation. In this set-up, we formulate the algorithm design as a robust control problem, showing that it yields a fully distributed algorithm. We also provide a distributed routine to acquire the internal model. We show that the algorithm converges exactly to the sequence of optimal solutions. We empirically evaluate the performance of the algorithm for different choices of parameters. Additionally, we evaluate the performance of the algorithm for quadratic problems with inexact internal model and non-quadratic problems, and show that it outperforms alternative algorithms in both scenarios.