Distributed stochastic gradient tracking algorithm with variance reduction for non-convex optimization

TL;DR

This paper introduces a distributed stochastic gradient tracking algorithm with variance reduction for non-convex optimization, achieving faster convergence and lower complexity in multi-agent network settings.

Contribution

It develops a novel GT-VR algorithm combining gradient tracking and variance reduction, with proven convergence to stationary points and improved complexity over existing methods.

Findings

Converges to first-order stationary points at O(1/k) rate.

Lower gradient complexity than existing methods under mild conditions.

Experimental results verify efficiency and effectiveness.

Abstract

This paper proposes a distributed stochastic algorithm with variance reduction for general smooth non-convex finite-sum optimization, which has wide applications in signal processing and machine learning communities. In distributed setting, large number of samples are allocated to multiple agents in the network. Each agent computes local stochastic gradient and communicates with its neighbors to seek for the global optimum. In this paper, we develop a modified variance reduction technique to deal with the variance introduced by stochastic gradients. Combining gradient tracking and variance reduction techniques, this paper proposes a distributed stochastic algorithm, GT-VR, to solve large-scale non-convex finite-sum optimization over multi-agent networks. A complete and rigorous proof shows that the GT-VR algorithm converges to first-order stationary points with $O(\frac{1}{k})$ convergence rate. In addition, we provide the complexity analysis of the proposed algorithm. Compared with some existing first-order methods, the proposed algorithm has a lower $\mathcal{O}(PM\epsilon^{-1})$ gradient complexity under some mild condition. By comparing state-of-the-art algorithms and GT-VR in experimental simulations, we verify the efficiency of the proposed algorithm.