Robust Predict-Then-Optimize Handles Feature Perturbations

Traditional integrated learning and optimization models, often referred to as "predict-then-optimize," typically assume that side information or features are perfectly accurate. However, in real-world scenarios, empirical data-driven features are frequently noisy, corrupted, or subject to disturbances at the point of decision-making. This can lead to fragile operational policies and suboptimal outcomes. To bridge this critical gap, this research proposes a "smart predict-then-robustly-optimize" framework. This novel approach directly integrates principles of robust optimization into the predictive-prescriptive pipeline. It achieves this through a specialized loss function designed to hedge against worst-case feature perturbations, ensuring that the resulting operational policies are resilient to real-world data imperfections. The paper establishes a computationally tractable convex surrogate for this robust loss, proving its structural validity with an exponentially decaying approximation error probability. Furthermore, it demonstrates that this framework is Fisher consistent with high probability under mild assumptions. Numerical experiments consistently validate that this robust approach yields significant performance improvements over standard predict-then-optimize methods, both in out-of-sample performance and training stability, even when standard methods employ regularized predictions.