Sample average approximations of strongly convex stochastic programs in Hilbert spaces

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