🤖 AI Summary
This work addresses the limitations of traditional predict-then-optimize approaches, which ignore prediction uncertainty, and existing distributionally robust optimization (DRO) methods that employ fixed-radius ambiguity sets ill-suited for dynamic risk environments. The authors propose a Learnable Prediction Ambiguity Set (LPAS), which jointly learns the center, state-dependent Wasserstein radius, and anisotropic metric of the ambiguity set. This is achieved through end-to-end joint optimization of a deep contextual model and the downstream decision layer, enhanced by conditional quantile calibration and scale regularization to enable state-adaptive robustness. Evaluated on S&P 500 portfolio optimization from 2018 to 2026, LPAS achieves an annualized return of 26.28%, a Sharpe ratio of 1.30, a terminal wealth of 1.61, lower tail risk, and a smaller average ambiguity set radius compared to benchmarks.
📝 Abstract
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.