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[2602.16148] Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration
Summary
This paper introduces FlexATC, a communication-efficient framework for distributed nonsmooth optimization, achieving notable convergence rates and communication acceleration.
Why It Matters
The study addresses a critical challenge in distributed optimization by proposing a novel algorithm that enhances communication efficiency, which is vital for large-scale machine learning applications. The findings can significantly impact how distributed systems are designed, potentially leading to faster and more efficient algorithms in practice.
Key Takeaways
- FlexATC unifies various ATC-based distributed algorithms for optimization.
- The framework achieves sublinear and linear convergence rates independent of network topology.
- Local updates can skip communication in most iterations without degrading performance.
Mathematics > Optimization and Control arXiv:2602.16148 (math) [Submitted on 18 Feb 2026] Title:Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration Authors:Luyao Guo, Xinli Shi, Wenying Xu, Jinde Cao View a PDF of the paper titled Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration, by Luyao Guo and 3 other authors View PDF HTML (experimental) 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 experiment...
