用机器学习构建更小的不确定集，提升约束优化的可靠性
From Data to Uncertainty Sets: a Machine Learning Approach
- 基于模型损失函数构造不确定性集合，缩小预测误差范围
- 实验显示不确定集半径比其他方法小一个数量级
- 适合需要高可靠性约束的决策优化场景
现有预测性分析方法通常仅优化目标函数的期望值，但在处理不确定约束时效果不佳，因期望满足不等于低违规概率。为此，本文采用鲁棒优化思想，基于机器学习模型的损失函数设计不确定性集，旨在最小化预测周围的不确定性。通过借鉴鲁棒优化理论，推导出严格的违规概率保证。在合成计算实验中，该方法所需的不确定性集半径比现有方法小一个数量级，显著提升了优化方案的稳健性。
原文摘要 · Abstract (English)
Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches.
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