S-NEAR-DGD: A Flexible Distributed Stochastic Gradient Method for Inexact Communication

TL;DR

S-NEAR-DGD is a flexible distributed stochastic gradient method designed to handle inexact computation and communication, ensuring linear convergence to a neighborhood of the optimal solution in large-scale systems.

Contribution

The paper introduces S-NEAR-DGD, a novel distributed stochastic gradient algorithm that tolerates inexact communication and computation, with proven convergence guarantees.

Findings

Converges linearly in expectation for strongly convex functions.

Neighborhood size depends on communication quality and gradient approximation accuracy.

Numerical results demonstrate practical effectiveness of the method.

Abstract

We present and analyze a stochastic distributed method (S-NEAR-DGD) that can tolerate inexact computation and inaccurate information exchange to alleviate the problems of costly gradient evaluations and bandwidth-limited communication in large-scale systems. Our method is based on a class of flexible, distributed first order algorithms that allow for the trade-off of computation and communication to best accommodate the application setting. We assume that all the information exchange between nodes is subject to random distortion and that only stochastic approximations of the true gradients are available. Our theoretical results prove that the proposed algorithm converges linearly in expectation to a neighborhood of the optimal solution for strongly convex objective functions with Lipschitz gradients. We characterize the dependence of this neighborhood on algorithm and network parameters, the quality of the communication channel and the precision of the stochastic gradient approximations used. Finally, we provide numerical results to evaluate the empirical performance of our method.