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arXiv · 1702.05122

Exact Diffusion for Distributed Optimization and Learning --- Part I: Algorithm Development

Kun Yuan·Bicheng Ying·Xiaochuan Zhao·Ali H. Sayed
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Abstract

This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range and superior convergence performance than the EXTRA strategy. The exact diffusion solution is applicable to non-symmetric left-stochastic combination matrices, while many earlier developments on exact consensus implementations are limited to doubly-stochastic matrices; these latter matrices impose stringent constraints on the network topology. The derivation of the exact diffusion strategy in this work relies on reformulating the aggregate optimization problem as a penalized problem and resorting to a diagonally-weighted incremental construction. Detailed stability and convergence analyses are pursued in Part II and are facilitated by examining the evolution of the error dynamics in a transformed domain. Numerical simulations illustrate the theoretical conclusions.

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Kun Yuan, Bicheng Ying, Xiaochuan Zhao, Ali H. Sayed. 2017-02-16. Exact Diffusion for Distributed Optimization and Learning --- Part I: Algorithm Development. https://arxiv.org/abs/1702.05122

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