Eco-PANDA: A Computationally Economic, Geometrically Converging, Dual Optimization Method on Time-Varying Undirected Graphs

TL;DR

Eco-PANDA is a new distributed optimization algorithm that reduces communication costs significantly while maintaining fast convergence rates on time-varying graphs, suitable for strongly convex problems.

Contribution

It introduces Eco-PANDA, a computationally economical variant of PANDA that halves communication costs and retains R-linear convergence on time-varying undirected graphs.

Findings

Halves communication costs compared to DIGing.

Maintains R-linear convergence rate.

Requires less computational effort per iteration.

Abstract

In this paper we consider distributed convex optimization over time-varying undirected graphs. We propose a linearized version of primarily averaged network dual ascent (PANDA) while requiring less computational costs. The proposed method, economic primarily averaged network dual ascent (Eco-PANDA), provably converges at R-linear rate to the optimal point given that the agents' objective functions are strongly convex and have Lipschitz continuous gradients. Therefore, the method is competitive, in terms of type of rate, with both DIGing and PANDA. The proposed method halves the communication costs of methods like DIGing while still converging R-linearly and having the same per iterate complexity.