Distributed stochastic projection-free solver for constrained optimization

TL;DR

This paper introduces a distributed stochastic projection-free optimization algorithm that efficiently handles large-scale constrained problems by combining variance reduction and gradient tracking, ensuring convergence with favorable complexity.

Contribution

It presents a novel distributed stochastic Frank-Wolfe algorithm with variance reduction and gradient tracking, improving convergence and efficiency for complex constrained optimization.

Findings

Converges with a sublinear rate for convex and non-convex problems.

Achieves superior complexity guarantees compared to existing methods.

Demonstrates effective convergence and computational efficiency in simulations.

Abstract

This paper proposes a distributed stochastic projection-free algorithm for large-scale constrained finite-sum optimization whose constraint set is complicated such that the projection onto the constraint set can be expensive. The global cost function is allocated to multiple agents, each of which computes its local stochastic gradients and communicates with its neighbors to solve the global problem. Stochastic gradient methods enable low computational cost, while they are hard and slow to converge due to the variance caused by random sampling. To construct a convergent distributed stochastic projection-free algorithm, this paper incorporates a variance reduction technique and gradient tracking technique in the Frank-Wolfe update. We develop a sampling rule for the variance reduction technique to reduce the variance introduced by stochastic gradients. Complete and rigorous proofs show that the proposed distributed projection-free algorithm converges with a sublinear convergence rate and enjoys superior complexity guarantees for both convex and non-convex objective functions. By comparative simulations, we demonstrate the convergence and computational efficiency of the proposed algorithm.