Tightly Robust Optimization via Empirical Domain Reduction

Abstract

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/n), whereas the scale obtained by a standard approach is O(d/n). This means that our algorithm is less affected by the dimensionality of the parameters.

Tasks

Reproductions