GENERAL FEASIBILITY BOUNDS FOR SAMPLE AVERAGE APPROXIMATION VIA VAPNIK-CHERVONENKIS DIMENSION

We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programs without relatively complete recourse. We utilize results from the Vapnik--Chervonenkis (VC) dimension and probably approximately correct learning to provide a general framework to construct feasibility bounds for SAA solutions under minimal structural or distributional assumption. We show that, as long as the hypothesis class formed by the feasible region has a finite VC dimension, the infeasibility of SAA solutions decreases exponentially with computable rates and explicitly identifiable accompanying constants. We demonstrate how our bounds apply more generally and competitively compared to existing results.