Distributed Online Randomized Gradient-Free Optimization with Compressed Communication

TL;DR

This paper introduces a unified framework for distributed online convex optimization that reduces communication costs using data compression and gradient estimation techniques, while maintaining convergence guarantees.

Contribution

It proposes the Online Compressed Gradient Tracking framework with two variants, integrating compression and gradient-free or stochastic gradient methods for efficient distributed optimization.

Findings

Achieves low dynamic regret in distributed settings.

Reduces communication overhead significantly.

Maintains convergence guarantees under practical constraints.

Abstract

This paper addresses two fundamental challenges in distributed online convex optimization: communication efficiency and optimization under limited feedback. We propose a unified framework named Online Compressed Gradient Tracking (OCGT), which includes two variants: One-point Bandit Feedback (OCGT-BF) and Stochastic Gradient Feedback (OCSGT). The proposed algorithms harness data compression and either gradient-free or stochastic gradient optimization techniques within distributed networks. The proposed framework incorporates a compression scheme with error compensation mechanisms to reduce communication overhead while maintaining convergence guarantees. Unlike traditional approaches that assume perfect communication and full gradient access, OCGT operates effectively under practical constraints by combining gradient-like tracking with one-point or stochastic gradient feedback estimation. We provide a theoretical analysis demonstrating dynamic regret bounds for both variants. Finally, extensive experiments validate that OCGT achieves low dynamic regret while significantly reducing communication requirements.