AsySPA: An Exact Asynchronous Algorithm for Convex Optimization Over Digraphs

Jiaqi Zhang

doi:10.1109/TAC.2019.2930234

Return

AsySPA: An Exact Asynchronous Algorithm for Convex Optimization Over Digraphs

2020-06-01

Jiaqi Zhang

游

游科友 (Keyou You) *

DOI：10.1109/TAC.2019.2930234

Original

Save

View PDF

Abstract

En 中文

This paper proposes a novel exact asynchronous subgradient-push algorithm (AsySPA) to solve an additive cost optimization problem over digraphs where each node only has access to a local convex function and updates asynchronously with an arbitrary rate. Specifically, each node of a strongly connected digraph does not wait for updates from other nodes but simply starts a new update within any bounded time interval by using local information available from its in-neighbors. Exact means that every node of the AsySPA can asymptotically converge to the same optimal solution, even under different update rates among nodes and bounded communication delays. To address uneven update rates, we design a simple mechanism to adaptively adjust stepsizes per update in each node, which is substantially different from the existing works. Then, we construct a delay-free augmented system to address asynchrony and delays, and study its convergence by proposing a generalized subgradient algorithm, which clearly has its own significance and helps us to explicitly evaluate the convergence rate of the AsySPA. Finally, we demonstrate advantages of the AsySPA in both theory and simulation.

Keywords:

Delays

Convergence

Optimization

Synchronization

Convex functions

Clocks

Distributed algorithms

Asynchronous subgradient-push algorithm (AsySPA)

distributed optimization problem (DOP)

even update rates (EUR)

uneven update rates (UUR)

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.