Distributed Evolution Strategies for Black-box Stochastic Optimization

TL;DR

This paper introduces a distributed evolution strategy (DES) for black-box stochastic optimization, achieving competitive convergence rates and improved efficiency by leveraging a Gaussian model and adaptive sampling schemes.

Contribution

The paper proposes a novel distributed evolution strategy that combines classic evolutionary algorithms with distributed frameworks, improving convergence and efficiency in black-box optimization.

Findings

DES has convergence rates competitive with zeroth-order methods.

The method exploits sparsity to match first-order methods.

Simulation results show reduced convergence time and increased robustness.

Abstract

This work concerns the evolutionary approaches to distributed stochastic black-box optimization, in which each worker can individually solve an approximation of the problem with nature-inspired algorithms. We propose a distributed evolution strategy (DES) algorithm grounded on a proper modification to evolution strategies, a family of classic evolutionary algorithms, as well as a careful combination with existing distributed frameworks. On smooth and nonconvex landscapes, DES has a convergence rate competitive to existing zeroth-order methods, and can exploit the sparsity, if applicable, to match the rate of first-order methods. The DES method uses a Gaussian probability model to guide the search and avoids the numerical issue resulted from finite-difference techniques in existing zeroth-order methods. The DES method is also fully adaptive to the problem landscape, as its convergence is guaranteed with any parameter setting. We further propose two alternative sampling schemes which significantly improve the sampling efficiency while leading to similar performance. Simulation studies on several machine learning problems suggest that the proposed methods show much promise in reducing the convergence time and improving the robustness to parameter settings.