Distributed Primal-dual Optimization for Heterogeneous Multi-agent Systems

TL;DR

This paper introduces an asynchronous distributed primal-dual optimization algorithm tailored for heterogeneous multi-agent systems, enabling agents to choose different update schemes and ensuring efficient convergence.

Contribution

It presents a novel hybrid optimization framework that allows agent-dependent updates and proves global linear convergence under broad conditions.

Findings

Algorithm achieves linear convergence in expectation.

Heterogeneous agents can effectively coordinate with different update schemes.

Numerical experiments demonstrate practical efficiency and robustness.

Abstract

Heterogeneous networks comprise agents with varying capabilities in terms of computation, storage, and communication. In such settings, it is crucial to factor in the operating characteristics in allowing agents to choose appropriate updating schemes, so as to better distribute computational tasks and utilize the network more efficiently. We consider the multi-agent optimization problem of cooperatively minimizing the sum of local strongly convex objectives. We propose an asynchronous distributed primal-dual protocol, which allows for the primal update steps to be agent-dependent (an agent can opt between first-order or Newton updates). Our analysis introduces a unifying framework for such hybrid optimization scheme and establishes global linear convergence in expectation, under strongly convex objectives and general agent activation schemes. Numerical experiments on real life datasets attest to the merits of the proposed algorithm.