PANDA: A Dual Linearly Converging Method for Distributed Optimization over Time-Varying Undirected Graphs

TL;DR

This paper introduces PANDA, a dual method for distributed convex optimization over dynamic networks, achieving faster convergence with fewer communications and demonstrated improved practical performance.

Contribution

PANDA is a novel dual algorithm that converges linearly over time-varying graphs, reducing communication costs compared to existing methods like DIGing.

Findings

Achieves R-linear convergence under strong convexity and Lipschitz conditions.

Requires half the variable exchanges per iteration compared to DIGing.

Empirically demonstrates improved practical performance.

Abstract

In this paper we consider a distributed convex optimization problem over time-varying networks. We propose a dual method that converges R-linearly to the optimal point given that the agents' objective functions are strongly convex and have Lipschitz continuous gradients. The proposed method requires half the amount of variable exchanges per iterate than methods based on DIGing, and yields improved practical performance as empirically demonstrated.