A geometrically converging dual method for distributed optimization over time-varying graphs

TL;DR

This paper introduces PANDA, a dual method for distributed convex optimization over dynamic networks, which converges linearly under certain conditions and reduces communication compared to existing methods.

Contribution

The paper proposes PANDA, a novel dual algorithm for distributed optimization over time-varying graphs with proven linear convergence and improved communication efficiency.

Findings

PANDA converges R-linearly to the optimal solution.

PANDA requires half the variable exchanges per iteration compared to DIGing-based methods.

Empirical results show practical performance improvements.

Abstract

In this paper we consider a distributed convex optimization problem over time-varying undirected networks. We propose a dual method, primarily averaged network dual ascent (PANDA), that is proven to converge R-linearly to the optimal point given that the agents objective functions are strongly convex and have Lipschitz continuous gradients. Like dual decomposition, PANDA requires half the amount of variable exchanges per iterate of methods based on DIGing, and can provide with practical improved performance as empirically demonstrated.