标题： 分布鲁棒优化是一个多目标问题 显示英文标题

标题： Distributionally Robust Optimization is a Multi-Objective Problem

摘要： 分布鲁棒优化（DRO）是在存在模型不确定性时进行决策的最坏情况方法。 尽管被表述为一个单目标问题，我们表明它本质上是多目标的，因为DRO解在期望成本和称为最坏情况敏感性（WCS）的鲁棒性度量之间绘制出一个接近帕累托最优的前沿。 我们将这一点作为起点，通过多目标的视角来探索鲁棒决策。 我们证明WCS是一个分散度的度量，并推导了在DRO中常用的不确定性集集合的WCS。 这些敏感度度量识别出名义期望成本最容易受到的误差，以及最有效地缓解这些误差的最坏情况问题的不确定性集。 相关的均值-敏感度前沿用于选择其大小。 多目标视角提供了一个鲁棒性的定量度量，并提供了一种基于敏感度的方法来解决DRO中的重要概念差距——如何为给定的成本分布选择不确定性集的族和大小，以及这如何影响解决方案。 显示英文摘要

摘要： Distributionally Robust Optimization (DRO) is a worst-case approach to decision making when there is model uncertainty. Though formulated as a single-objective problem, we show that it is intrinsically multi-objective in that DRO solutions map out a near-Pareto-optimal frontier between expected cost and a measure of robustness called worst-case sensitivity (WCS). We take this as the starting point and explore robust decision making through a multi-objective lens. We show that WCS is a measure of spread and derive WCS for a collection of uncertainty sets commonly used in DRO. These sensitivity measures identify the errors against which the nominal expected cost is most vulnerable and the uncertainty set for the worst-case problem that most effectively mitigates it. The associated mean-sensitivity frontier is used to select its size. The multi-objective perspective provides a quantitative measure of robustness and a sensitivity-based approach to addressing important conceptual gaps in DRO -- how to choose the family and size of uncertainty sets for a given cost distribution, and how this affects the solution.