Decentralized Asynchronous Nonconvex Stochastic Optimization on Directed Graphs

In this article, we consider a decentralized stochastic optimization problem over a network of agents, modeled as a directed graph: Agents aim to asynchronously minimize the average of their individual losses (possibly nonconvex), each one having access only to a noisy estimate of the gradient of its own function. We propose an asynchronous distributed algorithm for such a class of problems. The algorithm combines stochastic gradients with tracking in an asynchronous push-sum framework and obtains a sublinear convergence rate, matching the rate of the centralized stochastic gradient descent applied to the nonconvex minimization. Our experiments on a nonconvex image classification task using a convolutional neural network validate the convergence of our proposed algorithm across a different number of nodes and graph connectivity percentages.