Gradient-Based Multiple Robust Learning Calibration on Data Missing-Not-at-Random via Bi-Level Optimization
Shuxia Gong, Chen Ma · Entropy · 2025
Recommendation systems (RS) have become integral to numerous digital platforms and applications, ranging from e-commerce to content streaming field. A critical problem in RS is that the ratings are missing not at random (MNAR), which is due to the users always giving feedback on items with self-selection. The biased selection of rating data results in inaccurate rating prediction for all user-item pairs. Doubly robust (DR) learning has been studied in many tasks in RS, which is unbiased when either a single imputation or a single propensity model is accurate. In addition, multiple robust (MR) has been proposed with multiple imputation models and propensity models, and is unbiased when there exists a linear combination of these imputation models and propensity models is correct. However, we claim that the imputed errors and propensity scores are miscalibrated in the MR method. In this paper, we propose a gradient-based calibrated multiple robust learning method to enhance the debiasing performance and reliability of the rating prediction model. Specifically, we propose to use bi-level optimization to solve the weights and model coefficients of each propensity and imputation model in MR framework. Moreover, we adopt the differentiable expected calibration error as part of the objective to optimize the model calibration quality directly. Experiments on three real-world datasets show that our method outperforms the state-of-the-art baselines.