A Two-timescale Primal-dual Algorithm for Decentralized Optimization with Compression

TL;DR

This paper introduces TiCoPD, a two-timescale primal-dual algorithm with compression for decentralized optimization, achieving efficient communication and convergence guarantees, validated through neural network training experiments.

Contribution

The paper presents a novel two-timescale primal-dual algorithm with compression for decentralized optimization, improving communication efficiency and convergence analysis.

Findings

Converges with a constant step size.

Achieves an O(1/T) stationary solution after T iterations.

Validated on neural network training tasks.

Abstract

This paper proposes a two-timescale compressed primal-dual (TiCoPD) algorithm for decentralized optimization with improved communication efficiency over prior works on primal-dual decentralized optimization. The algorithm is built upon the primal-dual optimization framework and utilizes a majorization-minimization procedure. The latter naturally suggests the agents to share a compressed difference term during the iteration. Furthermore, the TiCoPD algorithm incorporates a fast timescale mirror sequence for agent consensus on nonlinearly compressed terms, together with a slow timescale primal-dual recursion for optimizing the objective function. We show that the TiCoPD algorithm converges with a constant step size. It also finds an O(1 /T ) stationary solution after T iterations. Numerical experiments on decentralized training of a neural network validate the efficacy of TiCoPD algorithm.