2025/04/05 by Natthawut Boonsiriphatthanajaroen, Boonsiriphatthanajaroen, Natthawut, Shane G. Henderson +1
Computer Science · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Optimization and Control (math.OC) #Privacy-Preserving Technologies in Data #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2504.04213
openalex publication_date 2025/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the convergence properties of the original and away-step Frank-Wolfe algorithms for linearly constrained stochastic optimization assuming the availability of unbiased objective function gradient estimates. The objective function is not restricted to a finite summation form, like in previous analyses tailored to machine-learning applications. To enable the use of concentration inequalities we assume either a uniform bound on the variance of gradient estimates or uniformly sub-Gaussian tails on gradient estimates. With one of these regularity assumptions along with sufficient sampling, we can ensure sufficiently accurate gradient estimates. We then use a Lyapunov argument to obtain the desired complexity bounds, relying on existing geometrical results for polytopes.