Sample Average Approximations of Strongly Convex Stochastic Programs in Hilbert Spaces
Abstract
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 nonasymptotic 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 infinitedimensional optimization problems governed by affinelinear partial differential equations with random inputs.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2104.05114
 Bibcode:
 2021arXiv210405114M
 Keywords:

 Mathematics  Optimization and Control;
 90C15;
 49N10
 EPrint:
 15 pages