Unified Minimax Optimization Framework for Propensity Score Estimation in Debiased Recommendation

Recommendation systems commonly face selection bias from missing-not-at-random (MNAR) collected data. To address this bias, propensity-based methods such as inverse propensity scoring (IPS) and doubly robust (DR) estimators are widely used. In addition, many methods extend the vanilla IPS and DR to further control the bias, variance, propensity mis-calibration, and imbalance, but they only optimize some of the above metrics, limiting the debiasing performance. In this paper, we first empirically find that controlling one metric cannot guarantee the control of other important metrics, then we reveal a fundamental structural commonality among the above four important metrics, and propose a Unified Propensity Optimization (UPO) framework that optimizes all metrics simultaneously by a minimax optimization algorithm. Theoretically, we demonstrate that minimizing the UPO loss effectively controls all metrics, ensuring their simultaneous improvements without incurring additional bias, and achieving reduced variance compared to naively adding up multiple control losses in penalty terms. Empirically, experiments on a semi-synthetic dataset and three real-world datasets validate UPO’s effectiveness, demonstrating superior performance compared to state-of-the-art methods with minor computational overhead. We fully open-source our code.