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.
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