GTAdam: Gradient Tracking With Adaptive Momentum for Distributed Online Optimization

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