A Minimax Approach for Optimal Incentive Policy Learning

Music City Center 

While strategic incentive policies are essential in personalized services, variations in user responses and revenue potentials create significant challenges in identifying optimal incentive policies. Existing literature typically falls short in fully identification of all user types and often assumes a uniform conversion revenue, leading to inefficient incentive allocations. In this study, we propose a minimax policy learning approach within a counterfactual principal strata framework. A value function, accommodating varying rewards across six potentially non-identifiable principal strata, is designed to minimize the worst-case value loss relative to three alternative policies: never-treat, always-treat, and oracle. To learn an optimal policy, we introduce three estimators: Principal Outcome Regression (P-OR), Principal Inverse Propensity Scoring (P-IPS), and Principal Doubly Robust (P-DR), providing theoretical guarantees for their unbiasedness, robustness, and regret upper bound. Extensive numerical experiments validate the effectiveness and superiority of our proposed approach.

Policy learning

Minimax

Counterfactual principal strata

Partial identification

Causal inference 

International Chinese Statistical Association