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Nash Equilibria, Regularization, and Computation in Optimal Transport-Based Distributionally Robust Optimization

Soroosh Shafiee¹; Liviu Aolaritei²; Florian Dörfler³; Daniel Kuhn⁴

¹ Operations Research and Information Engineering, Cornell University, Ithaca, New York 14850 · ² Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, California 94720 · ³ Automatic Control Lab, Eidgenössische Technische Hochschule Zürich, 8092 Zürich, Switzerland · ⁴ Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

Nature Doesn’t Play Dice, It Plays to Win Decision making under uncertainty can be brittle, often failing when real-world data deviates from training assumptions. This study frames this problem as a game between a decision maker and an adversary, nature, who strategically corrupts the data distribution to create a worst case scenario with the cost of these changes defined by optimal transport theory. The authors establish conditions under which a stable outcome, a Nash equilibrium, exists and provide efficient methods to compute it. A key insight is that nature’s optimal strategy corresponds to generating remarkably deceptive adversarial examples; in an image classification task, this strategy can transform an image of an “8” into a convincing “3.” This work provides a powerful framework for developing more reliable models by understanding and countering worst case data perturbations.

DOI

10.1287/opre.2023.0138

Volume

74 (3)

Pages

1689-1709

Language

en

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