论文标题
通过降低经验领域的紧密优化优化
Tightly Robust Optimization via Empirical Domain Reduction
论文作者
论文摘要
数据驱动的决策是通过解决参数化优化问题来执行的，并且最佳决策是通过最佳解决方案给出的未知真实参数。即使这些解决方案未知，我们通常也需要一个满足真正约束的解决方案。使用强大的优化来获得这种解决方案，其中参数的不确定性由椭圆形表示，并且稳健性的尺度由系数控制。在这项研究中，我们提出了一种算法来确定量表，以使解决方案具有良好的客观值并以给定的置信度概率满足真正的约束。在某些规律性条件下，我们的算法获得的比例渐近$ o（1/\ sqrt {n}）$，而标准方法获得的比例为$ O（\ sqrt {d/n}）$。这意味着我们的算法受参数维度的影响较小。
Data-driven decision-making is performed by solving a parameterized optimization problem, and the optimal decision is given by an optimal solution for unknown true parameters. We often need a solution that satisfies true constraints even though these are unknown. Robust optimization is employed to obtain such a solution, where the uncertainty of the parameter is represented by an ellipsoid, and the scale of robustness is controlled by a coefficient. In this study, we propose an algorithm to determine the scale such that the solution has a good objective value and satisfies the true constraints with a given confidence probability. Under some regularity conditions, the scale obtained by our algorithm is asymptotically $O(1/\sqrt{n})$, whereas the scale obtained by a standard approach is $O(\sqrt{d/n})$. This means that our algorithm is less affected by the dimensionality of the parameters.
