Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization

Predict-then-optimize systems usually compress uncertainty into a point forecast and then solve a downstream optimization problem as if the forecast were reliable. Distributionally robust optimization (DRO) offers protection against misspecification, but the ambiguity set is often centered at historical samples and uses a fixed radius. We propose \emph{learned predictive ambiguity sets} (LPAS): a deep contextual model outputs a finite nominal scenario distribution, a state-dependent Wasserstein radius, and optionally an anisotropic ground metric. These outputs define a contextual ambiguity set that feeds a DRO decision layer. The radius is trained by a combination of conditional quantile calibration, size regularization, and downstream decision loss, so that robustness is adaptive rather than globally fixed. We derive the finite dual form used by the decision layer, present a staged training algorithm, and evaluate the method on distributionally robust portfolio optimization with 20 S&P 500 constituents from 2018--2026. The proposed method substantially improves over equal-weight, predict-then-optimize, and historical Wasserstein DRO baselines, achieving 26.28% annualized return, Sharpe ratio 1.30, final wealth 1.61, and lower tail loss than a deep fixed-radius DRO baseline while using a smaller average radius. The results show that learned ambiguity radii can recover most of the performance of strong fixed-radius DRO while reducing unnecessary conservatism and improving regime adaptivity.