Vapnik-Chervonenkis维数下样本平均近似的一般可行界
General Feasibility Bounds for Sample Average Approximation via Vapnik-Chervonenkis Dimension
摘要：
本文研究了样本平均近似（SAA）在一般随机最优化问题中的可行性，包括在没有相对完全补偿假设的情况下的两阶段随机规划问题。我们利用Vapnik-Chervonenkis（VC）维度和可能近似正确学习的结果，而不是分析具有特定结构的问题，以提供一个通用框架，该框架在最小的结构或分布假设下为SAA解决方案提供明确的可行性界限。我们表明，只要假设类形成的feasbible区域具有有限的VC维，SAA解决方案的不可行性呈指数下降与可计算的速率和明确识别的伴随常数。我们展示了我们的界限如何适用于更普遍和竞争力相比，现有的结果。
英文摘要：
We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse assumption. Instead of analyzing problems with specific structures, we utilize results from the Vapnik-Chervonenkis (VC) dimension and Probably Approximately Correct learning to provide a general framework that offers explicit feasibility bounds for SAA solutions under minimal structural or distributional assumption. We show that, as long as the hypothesis class formed by the feasbible 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.
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