Decentralized Asynchronous Non-convex Stochastic Optimization on Directed Graphs
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.
Cite
@article{arxiv.2110.10406,
title = {Decentralized Asynchronous Non-convex Stochastic Optimization on Directed Graphs},
author = {Vyacheslav Kungurtsev and Mahdi Morafah and Tara Javidi and Gesualdo Scutari},
journal= {arXiv preprint arXiv:2110.10406},
year = {2021}
}