Tightly Robust Optimization via Empirical Domain Reduction
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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.
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