An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems
It addresses the problem of scalable and robust optimisation for distributed agents in nonconvex settings, offering a novel asynchronous solution with proven convergence.
The paper tackles nonconvex decentralised optimisation over distributed networks by developing an asynchronous ADMM algorithm based on Randomised Block Coordinate Douglas-Rachford splitting, achieving convergence to first-order stationary solutions with demonstrated efficiency in distributed Phase Retrieval and sparse PCA problems.
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.