Distributed Stochastic Approximation with Local Projections

TL;DR

This paper introduces a distributed stochastic approximation method that maintains constraints within convex sets using local projections and a nonlinear gossip mechanism, enabling efficient consensus in networked systems.

Contribution

It presents a novel distributed algorithm combining stochastic approximation with local projections and nonlinear gossip, allowing constraint enforcement in networked environments.

Findings

The proposed method converges under certain conditions.

It effectively maintains constraints within convex sets.

The approach is scalable to large networks.

Abstract

We propose a distributed version of a stochastic approximation scheme constrained to remain in the intersection of a finite family of convex sets. The projection to the intersection of these sets is also computed in a distributed manner and a `nonlinear gossip' mechanism is employed to blend the projection iterations with the stochastic approximation using multiple time scales