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

Area of Science:

• Optimization Theory
• Distributed Systems
• Control Theory

Background:

• Distributed stochastic optimization (DSO) problems with complex constraints are challenging for traditional methods.
• Projected primal-dual methods often involve computationally expensive projection operations.

Purpose of the Study:

• To develop a computationally efficient algorithm for DSO with local set and coupled inequality constraints.
• To address the limitations of projected methods in handling complex constraints within a multiagent network.

Main Methods:

• The study proposes a distributed stochastic Frank-Wolfe primal-dual algorithm (DSFWPD).
• The algorithm combines recursive momentum and weighted averaging techniques.
• It operates within the Frank-Wolfe framework to avoid expensive projection operations.

Main Results:

• DSFWPD is the first stochastic Frank-Wolfe solver for DSO problems with coupled constraints.
• The algorithm achieves zero constraint violation on average.
• It demonstrates a sublinear decay of the optimality gap over directed, time-varying networks.

Conclusions:

• The proposed DSFWPD algorithm offers a computationally simpler and effective solution for a class of DSO problems.
• Numerical experiments validate the efficacy of the DSFWPD algorithm in practical scenarios.