Robust Pricing Policy Improvement with Invalid Instrumental Variables

We study offline policy improvement over a continuous price space when historical prices are endogenous and instrumental variables (IVs) are potentially invalid. Standard IV-based methods rely on instrument exogeneity. When this assumption is violated, the demand function cannot be identified, potentially leading to suboptimal pricing policies. To address this challenge, we relax the exact exogeneity assumption by constructing an ambiguity set of demand functions whose deviations from instrument exogeneity are bounded by a radius. We propose a robust policy that maximizes the worst-case expected revenue improvement over a baseline policy across this set. To overcome the computational challenge of the resulting max-min optimization, we derive a closed-form solution for the inner minimization problem. Furthermore, we develop a safe policy improvement procedure that maximizes the allowable violation radius of the ambiguity set subject to a prespecified worst-case revenue improvement. Theoretically, we establish convergence rates for the max-min policy regret and show that the proposed safe policy achieves the target revenue improvement up to a vanishing error. Simulation studies and synthetic dataset analysis in the context of airline-ticket pricing demonstrate the superior performance of our approach under instrument invalidity compared with existing methods.