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In recommender systems, users always choose the favorite items to rate, whichleads to data missing not at random and poses a great challenge for unbiasedevaluation and learning of prediction models. Currently, the doubly robust (DR)methods have been widely studied and demonstrate superior performance. However,in this paper, we show that DR methods are unstable and have unbounded bias,variance, and generalization bounds to extremely small propensities. Moreover,the fact that DR relies more on extrapolation will lead to suboptimalperformance. To address the above limitations while retaining doublerobustness, we propose a stabilized doubly robust (StableDR) learning approachwith a weaker reliance on extrapolation. Theoretical analysis shows thatStableDR has bounded bias, variance, and generalization error boundsimultaneously under inaccurate imputed errors and arbitrarily smallpropensities. In addition, we propose a novel learning approach for StableDRthat updates the imputation, propensity, and prediction models cyclically,achieving more stable and accurate predictions. Extensive experiments show thatour approaches significantly outperform the existing methods.

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