随机规划最优值的非渐近置信界
Non-asymptotic confidence bounds for the optimal value of a stochastic program
摘要：
讨论了建立随机最优化问题非渐近置信界的一般方法。我们的主要贡献是观察到，一个样本平均近似的问题提供的最优值的问题，这是本质上比相应的最优解的质量更好的上限和下界。同时，这样的界限比通过渐近方法获得的“标准”置信界限更可靠。讨论了MinMax随机最优化和随机约束问题的最优值的界。最后，我们的模拟研究说明了所提出的界限的数值行为。
英文摘要：
We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than "standard" confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a simulation study illustrating the numerical behavior of the proposed bounds.
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