  In recommender systems, users always choose the favorite items to rate, which
leads to data missing not at random and poses a great challenge for unbiased
evaluation 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 suboptimal
performance. To address the above limitations while retaining double
robustness, we propose a stabilized doubly robust (StableDR) learning approach
with a weaker reliance on extrapolation. Theoretical analysis shows that
StableDR has bounded bias, variance, and generalization error bound
simultaneously under inaccurate imputed errors and arbitrarily small
propensities. In addition, we propose a novel learning approach for StableDR
that updates the imputation, propensity, and prediction models cyclically,
achieving more stable and accurate predictions. Extensive experiments show that
our approaches significantly outperform the existing methods.
