GTAdam: Gradient Tracking with Adaptive Momentum for Distributed Online Optimization

TL;DR

This paper introduces GTAdam, a distributed online optimization algorithm that combines gradient tracking with adaptive momentum, achieving improved convergence and performance in multi-agent learning tasks.

Contribution

The paper proposes GTAdam, a novel distributed optimization algorithm that integrates gradient tracking with adaptive momentum estimation, enhancing convergence in online settings.

Findings

GTAdam guarantees linear convergence in static scenarios.

The algorithm achieves a bounded dynamic regret in online settings.

GTAdam outperforms existing methods in various numerical experiments.

Abstract

This paper deals with a network of computing agents aiming to solve an online optimization problem in a distributed fashion, i.e., by means of local computation and communication, without any central coordinator. We propose the gradient tracking with adaptive momentum estimation (GTAdam) distributed algorithm, which combines a gradient tracking mechanism with first and second order momentum estimates of the gradient. The algorithm is analyzed in the online setting for strongly convex cost functions with Lipschitz continuous gradients. We provide an upper bound for the dynamic regret given by a term related to the initial conditions and another term related to the temporal variations of the objective functions. Moreover, a linear convergence rate is guaranteed in the static setup. The algorithm is tested on a time-varying classification problem, on a (moving) target localization problem, and in a stochastic optimization setup from image classification. In these numerical experiments from multi-agent learning, GTAdam outperforms state-of-the-art distributed optimization methods.