The dual challenges of prohibitive communication overhead and the impracticality of gradient computation due to data privacy or black-box constraints in distributed systems motivate this work on communication-constrained gradient-free optimization. We propose a stochastic distributed zeroth-order algorithm (Com-DSZO) requiring only two function evaluations per iteration, integrated with general compression operators. Rigorous analysis establishes its sublinear convergence rate for both smooth and nonsmooth objectives, while explicitly elucidating the compression-convergence trade-off. Furthermore, we develop a variance-reduced variant (VR-Com-DSZO) under stochastic mini-batch feedback. The empirical algorithm performance are illustrated with numerical examples.
@article{arxiv.2503.17429,
title = {Distributed Stochastic Zeroth-Order Optimization with Compressed Communication},
author = {Youqing Hua and Shuai Liu and Yiguang Hong and Wei Ren},
journal= {arXiv preprint arXiv:2503.17429},
year = {2025}
}