  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.
