New Method Improves Portfolio Optimization with Adaptive Robustness.

Traditional predict-then-optimize systems often rely on single point forecasts, which can be unreliable. While Distributionally Robust Optimization (DRO) offers protection against forecast errors, its ambiguity sets are typically fixed. This paper proposes Learned Predictive Ambiguity Sets (LPAS), a novel approach that uses a deep contextual model to generate a finite nominal scenario distribution, a state-dependent Wasserstein radius, and an optional anisotropic ground metric. These elements define a contextual ambiguity set for a DRO decision layer. The key innovation is that the robustness radius is not fixed but is trained using a combination of conditional quantile calibration, size regularization, and downstream decision loss. This allows the system to adapt its robustness dynamically based on the context, avoiding unnecessary conservatism while maintaining protection. Evaluated on portfolio optimization with S&P 500 constituents, LPAS demonstrated substantial improvements over baselines, achieving higher annualized returns, Sharpe ratios, and final wealth, while also reducing tail loss and using a smaller average radius. This indicates that learned ambiguity radii can recover strong performance while being more efficient and adaptive to different market regimes.