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

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.