In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the prediction performance of models. Some existing estimators and regularizers attempt to achieve unbiased estimation to improve the predictive performance. However, variances and generalization bound of these methods are generally unbounded when the propensity scores tend to zero, compromising their stability and robustness. In this paper, we first theoretically reveal that limitations of regularization techniques. Besides, we further illustrate that, for more general estimators, unbiasedness will inevitably lead to unbounded variance. These general laws inspire us that the estimator designs is not merely about eliminating bias, reducing variance, or simply achieve a bias-variance trade-off. Instead, it involves a quantitative joint optimization of bias and variance. Then, we develop a systematic fine-grained dynamic learning framework to jointly optimize bias and variance, which adaptively selects an appropriate estimator for each user-item pair according to the predefined objective function. With this operation, the generalization bounds and variances of models are reduced and bounded with theoretical guarantees. Extensive experiments are conducted to verify the theoretical results and the effectiveness of the proposed dynamic learning framework.

翻译：在推荐系统、展示广告等大多数实际应用中，收集的数据常包含缺失值，且这些缺失值通常是非随机缺失的，这会降低模型的预测性能。现有的一些估计器和正则化方法试图通过无偏估计来提升预测性能。然而，当倾向得分趋近于零时，这些方法的方差与泛化界通常无界，从而损害了其稳定性与鲁棒性。本文首先从理论上揭示了正则化技术的局限性。此外，我们进一步证明对于更一般的估计器，无偏性将不可避免地导致无界方差。这些普遍规律启示我们：估计器设计不仅关乎消除偏差、降低方差或简单地实现偏差-方差权衡，更涉及偏差与方差的定量联合优化。为此，我们提出了一个系统性的细粒度动态学习框架来联合优化偏差与方差，该框架根据预设目标函数为每个用户-项目对自适应地选择合适的估计器。通过此操作，模型的泛化界与方差得以在理论保证下降低并保持有界。我们进行了大量实验以验证理论结果及所提动态学习框架的有效性。