Decentralized Asynchronous Non-convex Stochastic Optimization on Directed Graphs

TL;DR

This paper introduces an asynchronous decentralized algorithm for non-convex stochastic optimization on directed graphs, achieving convergence rates comparable to centralized methods, validated through neural network experiments.

Contribution

It proposes a novel asynchronous distributed algorithm combining stochastic gradients and tracking on directed graphs, with proven convergence for non-convex functions.

Findings

Achieves standard sublinear convergence rate for non-convex functions

Validates convergence through experiments on image classification tasks

Effective across various network sizes and connectivity levels

Abstract

Distributed Optimization is an increasingly important subject area with the rise of multi-agent control and optimization. We consider a decentralized stochastic optimization problem where the agents on a graph aim to asynchronously optimize a collective (additive) objective function consisting of agents' individual (possibly non-convex) local objective functions. Each agent only has access to a noisy estimate of the gradient of its own function (one component of the sum of objective functions). We proposed an asynchronous distributed algorithm for such a class of problems. The algorithm combines stochastic gradients with tracking in an asynchronous push-sum framework and obtain the standard sublinear convergence rate for general non-convex functions, matching the rate of centralized stochastic gradient descent SGD. Our experiments on a non-convex image classification task using convolutional neural network validate the convergence of our proposed algorithm across different number of nodes and graph connectivity percentages.