# Sample Average Approximations of Strongly Convex Stochastic Programs in Hilbert Spaces

arXiv: https://arxiv.org/abs/2104.05114 · HTML: https://mlsanity.com/paper/2104.05114/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2021.

## Built on by (most cited first, 4 of 4)

- [Metric Entropy-Free Sample Complexity Bounds for Sample Average Approximation in Convex Stochastic Programming](https://mlsanity.com/paper/2401.00664/) (2024)
- [Stochastic approximation in infinite dimensions](https://mlsanity.com/paper/2402.17258/) (2024)
- [Conditional Moment Kernels: Joint Modeling of Expected Returns and Covariances in Unbalanced Panels](https://mlsanity.com/paper/2410.21858/) (2024)
- [Revisiting Stochastic Approximation and Stochastic Gradient Descent](https://mlsanity.com/paper/2505.11343/) (2025)

## Abstract (arXiv)

We analyze the tail behavior of solutions to sample average approximations (SAAs) of stochastic programs posed in Hilbert spaces. We require that the integrand be strongly convex with the same convexity parameter for each realization. Combined with a standard condition from the literature on stochastic programming, we establish non-asymptotic exponential tail bounds for the distance between the SAA solutions and the stochastic program's solution, without assuming compactness of the feasible set. Our assumptions are verified on a class of infinite-dimensional optimization problems governed by affine-linear partial differential equations with random inputs. We present numerical results illustrating our theoretical findings.