A Parameter-Free Zeroth-Order Algorithm for Decentralized Stochastic Convex Optimization

TL;DR

This paper introduces D-POEM, a decentralized zeroth-order optimization algorithm that efficiently minimizes convex functions over networks using only noisy function evaluations, without prior knowledge of problem parameters.

Contribution

The paper presents a novel decentralized zeroth-order method that adaptively adjusts smoothing parameters, achieving improved convergence without requiring Lipschitz constant or diameter knowledge.

Findings

D-POEM outperforms existing distributed zeroth-order methods in experiments.

Theoretical convergence rate separates optimization and network disagreement terms.

Method adapts smoothing radius and stepsize without prior parameter knowledge.

Abstract

We consider decentralized stochastic convex optimization on connected network, in which gradients of agents are unavailable and each agent can query only noisy function values of its own local objective. The goal is to minimize the average objective over a compact convex domain using only local two point zeroth-order oracles and peer-to-peer communication. We propose a decentralized POEM method (D-POEM) that combines symmetric two point smoothing with adaptive radius and stepsize rules, thereby avoiding prior knowledge of the Lipschitz constant and diameter. For convex Lipschitz continuous objectives, we prove an convergence rate that separates a centralized optimization term from a network disagreement term. We further conduct the numerical experiments to demonstrate POEM outperforms existing distributed zeroth-order method.