  Post-click conversion, as a strong signal indicating the user preference, is
salutary for building recommender systems. However, accurately estimating the
post-click conversion rate (CVR) is challenging due to the selection bias,
i.e., the observed clicked events usually happen on users' preferred items.
Currently, most existing methods utilize counterfactual learning to debias
recommender systems. Among them, the doubly robust (DR) estimator has achieved
competitive performance by combining the error imputation based (EIB) estimator
and the inverse propensity score (IPS) estimator in a doubly robust way.
However, inaccurate error imputation may result in its higher variance than the
IPS estimator. Worse still, existing methods typically use simple
model-agnostic methods to estimate the imputation error, which are not
sufficient to approximate the dynamically changing model-correlated target
(i.e., the gradient direction of the prediction model). To solve these
problems, we first derive the bias and variance of the DR estimator. Based on
it, a more robust doubly robust (MRDR) estimator has been proposed to further
reduce its variance while retaining its double robustness. Moreover, we propose
a novel double learning approach for the MRDR estimator, which can convert the
error imputation into the general CVR estimation. Besides, we empirically
verify that the proposed learning scheme can further eliminate the high
variance problem of the imputation learning. To evaluate its effectiveness,
extensive experiments are conducted on a semi-synthetic dataset and two
real-world datasets. The results demonstrate the superiority of the proposed
approach over the state-of-the-art methods. The code is available at
https://github.com/guosyjlu/MRDR-DL.

Machine Learning;Information Retrieval