Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization

• 成果类型: Article
• 署名作者: Yu, Zhan; Ho, Daniel W. C.; Yuan, Deming
• 署名单位: City University of Hong Kong; Nanjing University of Science & Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3075669
• 发表日期: 2022
• 页码: 957-964
• 关键词: Convergence rate; distributed optimization; gradient-free methods; mirror descent; multiagent systems

摘要

This article is concerned with the multiagent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method is developed by introducing a randomized gradient-free oracle in the mirror descent scheme where the non-Euclidean Bregman divergence is used. The classical gradient descent method is generalized without using subgradient information of objective functions. The proposed algorithms are the first distributed non-Euclidean zeroth-order methods, which achieve an approximate O(1/root T) T-rate of convergence, recovering the best known optimal rate of distributed nonsmooth constrained convex optimization. Moreover, a decentralized reciprocal weighted averaging (RWA) approximating sequence is first investigated, the convergence for RWA sequence is shown to hold over time-varying graph. Rates of convergence are comprehensively explored for the algorithm with RWA (DRGFMD-RWA). The technique on constructing the decentralized RWA sequence provides new insight in searching for minimizers in distributed algorithms.