Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration

2026-02-17

AI Summary

This work addresses distributed composite optimization, where a network of agents collaboratively minimizes the sum of local smooth functions plus a common nonsmooth regularizer. The authors propose FlexATC, a communication-efficient adaptive-aggregation framework that employs a probabilistic local update mechanism and a unified stepsize policy independent of both the network topology and the number of local updates. Under strong convexity in an online setting, the theoretical analysis establishes, for the first time, that FlexATC achieves linear convergence with a rate decoupled from both the objective function and the network structure. This decoupling enables the majority of iterations to skip communication, yielding provable communication acceleration. Numerical experiments corroborate the theoretical findings, demonstrating sublinear and linear convergence rates in convex and strongly convex settings, respectively.

Technology Category

• Search and Optimization: Distributed Search
• Multiagent Systems: Agent Communication
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper is concerned with the distributed composite optimization problem over networks, where agents aim to minimize a sum of local smooth components and a common nonsmooth term. Leveraging the probabilistic local updates mechanism, we propose a communication-efficient Adapt-Then-Combine (ATC) framework, FlexATC, unifying numerous ATC-based distributed algorithms. Under stepsizes independent of the network topology and the number of local updates, we establish sublinear and linear convergence rates for FlexATC in convex and strongly convex settings, respectively. Remarkably, in the strong convex setting, the linear rate is decoupled from the objective functions and network topology, and FlexATC permits communication to be skipped in most iterations without any deterioration of the linear rate. In addition, the proposed unified theory demonstrates for the first time that local updates provably lead to communication acceleration for ATC-based distributed algorithms. Numerical experiments further validate the efficacy of the proposed framework and corroborate the theoretical results.

Problem

• distributed optimization
• nonsmooth optimization
• composite optimization
• local updates
• communication efficiency

Innovation

• distributed optimization
• local updates
• communication acceleration
• nonsmooth optimization
• linear convergence