1. Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization.
- Author
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Yu, Zhan, Ho, Daniel W. C., and Yuan, Deming
- Subjects
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CONSTRAINED optimization , *MATHEMATICAL optimization , *NONSMOOTH optimization , *DISTRIBUTED algorithms , *MIRRORS , *EUCLIDEAN algorithm , *APPROXIMATION algorithms , *LINEAR programming - Abstract
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 $O(\frac{1}{\sqrt{T}})$ $T$ -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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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