动态调整场景数量以精准控制风险，提升重复设计效率
Online Complexity Estimation for Repetitive Scenario Design
- 通过学习风险随样本量变化的分布函数，实时预测最优样本数
- 理论证明方法收敛，适用于固定复杂度场景问题
- 在非凸、时变分布等复杂场景中仍具高效性，适合工业重复设计
针对重复性场景设计问题，即需反复求解场景规划并调整样本规模（场景数量）以达到期望风险水平（约束违反概率），本文提出一种在线学习方法：基于历史场景解及其风险水平，学习风险随样本量变化的概率密度函数。一旦该函数建立，即可直接推导出最优样本量。我们证明了该方法对固定复杂度场景问题的正确性和收敛性，其涵盖广泛研究的全支撑凸场景规划问题。实验验证了方法在一系列具有挑战性的重复设计任务中的有效性，包括非固定复杂度、非凸约束及时间变化分布的情形。
原文摘要 · Abstract (English)
We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We propose an approach to learn on the fly the optimal sample size based on observed data consisting in previous scenario solutions and their risk level. Our approach consists in learning a function that represents the pdf (probability density function) of the risk as a function of the sample size. Once this function is known, retrieving the optimal sample size is straightforward. We prove the soundness and convergence of our approach to obtain the optimal sample size for the class of fixed-complexity scenario problems, which generalizes fully-supported convex scenario programs that have been studied extensively in the scenario optimization literature. We also demonstrate the practical efficiency of our approach on a series of challenging repetitive scenario design problems, including non-fixed-complexity problems, nonconvex constraints and time-varying distributions.
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