Stabilized Doubly Robust Learning for Recommendation on Data Missing Not at Random

In recommender systems, users always choose favorite items to rate, which results in data missing not at random and poses a great challenge for unbiased evaluation and learning of prediction models. Currently, the doubly robust (DR) method and its variants have been widely studied and demonstrate superior performance. However, we show that DR methods are unstable to extremely small propensities and rely on extrapolations, resulting in sub-optimal performances. In this paper, we propose a stabilized doubly robust (SDR) estimator to address the above limitations while retaining double robustness. Theoretical analysis shows that SDR has bounded bias, variance and generalization error bound under inaccurate imputed errors and arbitrarily small propensities. In addition, we propose a novel learning approach for SDR that updates the imputation, propensity, and prediction models cyclically, achieving more stable and accurate predictions. Extensive experiments show that our approach significantly outperforms the existing methods.