Prox-PDA: The Proximal Primal-Dual Algorithm for Fast Distributed Nonconvex Optimization and Learning Over Networks

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Mingyi Hong, Davood Hajinezhad, Ming-Min Zhao ;
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1529-1538, 2017.

Abstract

In this paper we consider nonconvex optimization and learning over a network of distributed nodes. We develop a Proximal Primal-Dual Algorithm (Prox-PDA), which enables the network nodes to distributedly and collectively compute the set of first-order stationary solutions in a global sublinear manner [with a rate of $O(1/r)$, where $r$ is the iteration counter]. To the best of our knowledge, this is the first algorithm that enables distributed nonconvex optimization with global rate guarantees. Our numerical experiments also demonstrate the effectiveness of the proposed algorithm.

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