Decentralized Asynchronous Non-convex Stochastic Optimization on Directed Graphs

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 non-convex), 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 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.