Distributed Frank-Wolfe Solver for Stochastic Optimization With Coupled Inequality Constraints

Abstract

Distributed stochastic optimization (DSO) with local set constraints and coupled inequality constraints over a multiagent network is considered in this article. Usually, such problems are tackled by projected primal-dual methods, which require expensive projection operations when set constraints are complicated. In this context, this article focuses on the Frank-Wolfe (FW) framework, which provides computational simplicity by avoiding expensive projection operations, for solving DSO with local set and coupled inequality constraints. By combining recursive momentum and weighted averaging, this article proposes a distributed stochastic FW primal-dual algorithm (DSFWPD), which is the first stochastic FW solver for DSO problems with coupled constraints. The proposed algorithm achieves zero constraint violation on average with a sublinear decay of the optimality gap over a directed and time-varying network. The efficacy of DSFWPD is demonstrated by several numerical experiments.