Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.04213 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909567291490304 |
|---|---|
| author | Boonsiriphatthanajaroen, Natthawut Henderson, Shane G. |
| author_facet | Boonsiriphatthanajaroen, Natthawut Henderson, Shane G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Convergence Analysis of Two Stochastic Frank-Wolfe Algorithms Boonsiriphatthanajaroen, Natthawut Henderson, Shane G. Optimization and Control 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. |
| title | A New Convergence Analysis of Two Stochastic Frank-Wolfe Algorithms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.04213 |