A Fast Distributed Proximal-Gradient Method

TL;DR

This paper introduces a distributed proximal-gradient algorithm with accelerated convergence for convex optimization over networks, improving efficiency in multi-agent systems with shared non-differentiable components.

Contribution

It proposes a novel distributed proximal-gradient method with Nesterov acceleration and multiple communication steps, achieving a faster convergence rate of 1/k.

Findings

Converges at rate 1/k, faster than existing methods.

Numerical experiments confirm the improved convergence.

Effective for networks with time-varying topology.

Abstract

We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has a favorable structure suitable for effective computation of the proximal operator. In our method, each agent iteratively updates its estimate of the global minimum by optimizing its local objective function, and exchanging estimates with others via communication in the network. Using Nesterov-type acceleration techniques and multiple communication steps per iteration, we show that this method converges at the rate 1/k (where k is the number of communication rounds between the agents), which is faster than the convergence rate of the existing distributed methods for solving this problem. The superior convergence rate of our method is also verified by numerical experiments.