首个可证明收敛的非凸分布式异步优化算法。
An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems
- 基于随机块坐标分裂法设计异步分布式算法。
- 可在非凸场景下找到一阶驻点，数值实验验证高效性。
- 适合分布式计算与异步通信场景下的优化任务。
本文研究网络中分布式代理的非凸分布式优化与学习问题。提出一种基于随机块坐标Douglas-Rachford分裂法的ADMM算法，使网络中的代理能分布式、异步地求解问题的一阶驻点。据我们所知，这是首个针对非凸优化问题具有收敛性证明的分布式异步算法。数值实验表明，该算法在分布式相位恢复和稀疏主成分分析问题上均表现出高效性。
原文摘要 · Abstract (English)
In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents in the network to distributedly and asynchronously compute a set of first-order stationary solutions of the problem. To the best of our knowledge, this is the first decentralised and asynchronous algorithm for solving nonconvex optimisation problems with convergence proof. The numerical examples demonstrate the efficiency of the proposed algorithm for distributed Phase Retrieval and sparse Principal Component Analysis problems.
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