Doubly Robust Distributionally Robust Offline Contextual Pricing

Offline contextual pricing often relies on logged observational data, but faces challenges from distributional shifts between training and deployment environments. Distributionally robust optimization (DRO) provides a principled approach to off-policy evaluation and learning (OPE/L). However, existing methods are mostly limited to discrete actions. Recent work has explored DRO for continuous treatments using inverse propensity weighting (IPW), while such IPW-based estimators can be sensitive to the convergence rate of propensity score estimates, particularly when estimated nonparametrically, which may lead to larger estimation errors and regret. In this work, we develop a doubly robust (DR) framework for distributionally robust OPE/L in continuous pricing settings. For evaluation, we propose a localized DR estimator that addresses the computational challenges of worst-case expectations by fitting only a small number of regressions, comparable to standard non-robust DR, while achieving semiparametric efficiency under mild product rate conditions. For learning, we leverage the inherent smoothness of demand noise to handle pricing-specific discontinuities in revenue outcomes (e.g., threshold-based purchase decisions), establishing a finite-sample regret bound of $\tilde{\mathcal{O}}_p(T^{-s/(2s+1)})$ for smoothness orders $s=1,2$. This bound improves upon existing regret rates in existing DRO-based off-policy learning (OPL) for continuous treatments. Extensive experiments under various levels of distribution shift validate our proposed framework.

Many companies want to set personalized prices using historical sales data, instead of running expensive live experiments on customers. These datasets record customer features, the price offered, and whether the purchase happened. As markets constantly change, such as customer tastes, competitors, and economic conditions, pricing strategies that have worked well in the past may perform poorly in the future. To address this, we developed a robust machine learning method that learns good personalized pricing rules from past data while preparing for unfavorable but realistic future market changes. Our approach carefully combines two sources of information: how prices were originally assigned in the historical data, and predictions of how much revenue different prices would generate. This “doubly robust” combination makes the evaluation much more stable, even when parts of the model are imperfect. Experiments on both simulated markets and real Expedia hotel booking data show that our method produces more reliable pricing strategies that maintain higher revenue under various market shifts compared to previous approaches.