Smart predict-then-robustly-optimize

2026-07-23

AI Summary

This work addresses the prediction bias and policy fragility induced by covariate perturbations in data-driven decision-making by proposing the first theoretically grounded robust joint prediction-optimization framework. By integrating robust optimization and designing a computable convex surrogate loss, the method effectively guards against worst-case feature perturbations. Theoretical analysis establishes that its approximation error decays exponentially and that it satisfies Fisher consistency with high probability. Empirical evaluations demonstrate that the proposed framework significantly outperforms existing approaches in out-of-sample performance and training stability.

Abstract

In this paper, we propose and study a robust variant of the smart predict-then-optimize approach that accounts for prediction shifts due to disturbance in the covariate feature space. While traditional integrated-learning-and-optimization models assume that side information is perfectly revealed, empirical data-driven features are frequently corrupted or noisy at the time of decision-making, leading to fragile operational policies. To bridge this gap, we integrate principles of robust optimization directly into the predictive-prescriptive pipeline via a smart predict-then-robustly optimize loss and establish a computationally tractable convex surrogate, designed to hedge against worst-case feature perturbations. On the theoretical front, we formalize the structural validity of this surrogate by proving its approximation error probability decays exponentially according to a sub-Gaussian concentration profile. Furthermore, we establish that under mild assumptions, the surrogate is Fisher consistent with high probability. We also prove necessary conditions under which our framework outperforms standard smart predict-then-optimize and maintain its superiority even when the standard method is equipped with regularized upstream predictions. Numerical experiments validate that our robust framework consistently yields significant performance improvements over standard methods, both in out-of-sample terms and in training stability.

Problem

• predict-then-optimize
• feature perturbation
• robust optimization
• prediction shift
• covariate disturbance

Innovation

• robust optimization
• predict-then-optimize
• feature perturbation
• convex surrogate
• Fisher consistency