Swarming for Faster Convergence in Stochastic Optimization

TL;DR

This paper introduces a distributed stochastic optimization method inspired by natural swarming behavior, which improves convergence speed over centralized algorithms, especially considering communication overhead and network connectivity.

Contribution

It proposes a novel swarming-inspired distributed stochastic gradient descent scheme with theoretical analysis of convergence and performance bounds.

Findings

Swarming-based approach outperforms centralized algorithms in convergence speed.

Error bounds decrease with network size and connectivity.

Finite-time performance characterized for convex and non-convex functions.

Abstract

We study a distributed framework for stochastic optimization which is inspired by models of collective motion found in nature (e.g., swarming) with mild communication requirements. Specifically, we analyze a scheme in which each one of $N > 1$ independent threads, implements in a distributed and unsynchronized fashion, a stochastic gradient-descent algorithm which is perturbed by a swarming potential. Assuming the overhead caused by synchronization is not negligible, we show the swarming-based approach exhibits better performance than a centralized algorithm (based upon the average of $N$ observations) in terms of (real-time) convergence speed. We also derive an error bound that is monotone decreasing in network size and connectivity. We characterize the scheme's finite-time performances for both convex and non-convex objective functions.