General Feasibility Bounds for Sample Average Approximation via Vapnik--Chervonenkis Dimension
研究了样本均值近似在一般随机优化问题中的可行性，利用VC维理论证明当可行域假设类VC维有限时，SAA解不可行性随样本量指数衰减，并给出可计算的速率和常数。
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.