Distributed Stochastic Nonconvex Optimization and Learning based on Successive Convex Approximation
This work addresses distributed optimization for multi-agent systems, offering a method for nonconvex problems with applications like neural network training, but it appears incremental as it builds on existing SCA techniques.
The paper tackles distributed stochastic nonconvex optimization in multi-agent networks by proposing a novel algorithmic framework based on successive convex approximation, achieving almost sure convergence to stationary solutions and demonstrating advantages in distributed neural network training through numerical results.
We study distributed stochastic nonconvex optimization in multi-agent networks. We introduce a novel algorithmic framework for the distributed minimization of the sum of the expected value of a smooth (possibly nonconvex) function (the agents' sum-utility) plus a convex (possibly nonsmooth) regularizer. The proposed method hinges on successive convex approximation (SCA) techniques, leveraging dynamic consensus as a mechanism to track the average gradient among the agents, and recursive averaging to recover the expected gradient of the sum-utility function. Almost sure convergence to (stationary) solutions of the nonconvex problem is established. Finally, the method is applied to distributed stochastic training of neural networks. Numerical results confirm the theoretical claims, and illustrate the advantages of the proposed method with respect to other methods available in the literature.