# Enhanced Doubly Robust Learning for Debiasing Post-click Conversion Rate Estimation

arXiv: https://arxiv.org/abs/2105.13623 · HTML: https://mlsanity.com/paper/2105.13623/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 28 May 2021.

## Builds on (most cited first, 15 of 15)

- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [Deep Interest Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1706.06978/) (2017)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [Entire Space Multi-Task Model: An Effective Approach for Estimating Post-Click Conversion Rate](https://mlsanity.com/paper/1804.07931/) (2018)
- [More Robust Doubly Robust Off-policy Evaluation](https://mlsanity.com/paper/1802.03493/) (2018)
- [Learning Intents behind Interactions with Knowledge Graph for Recommendation](https://mlsanity.com/paper/2102.07057/) (2021)
- [Reinforcement Learning to Optimize Long-term User Engagement in Recommender Systems](https://mlsanity.com/paper/1902.05570/) (2019)
- [Causal Embeddings for Recommendation](https://mlsanity.com/paper/1706.07639/) (2017)
- [Unbiased Recommender Learning from Missing-Not-At-Random Implicit Feedback](https://mlsanity.com/paper/1909.03601/) (2019)
- [Large-scale Causal Approaches to Debiasing Post-click Conversion Rate Estimation with Multi-task Learning](https://mlsanity.com/paper/1910.09337/) (2019)
- [Information Theoretic Counterfactual Learning from Missing-Not-At-Random Feedback](https://mlsanity.com/paper/2009.02623/) (2020)
- [Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption](https://mlsanity.com/paper/1910.12774/) (2019)
- [Asymmetric Tri-training for Debiasing Missing-Not-At-Random Explicit Feedback](https://mlsanity.com/paper/1910.01444/) (2019)

## Built on by (most cited first, 28 of 28)

- [ESCM2: Entire Space Counterfactual Multi-Task Model for Post-Click Conversion Rate Estimation](https://mlsanity.com/paper/2204.05125/) (2022)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [StableDR: Stabilized Doubly Robust Learning for Recommendation on Data Missing Not at Random](https://mlsanity.com/paper/2205.04701/) (2022)
- [TDR-CL: Targeted Doubly Robust Collaborative Learning for Debiased Recommendations](https://mlsanity.com/paper/2203.10258/) (2022)
- [A Generalized Doubly Robust Learning Framework for Debiasing Post-Click Conversion Rate Prediction](https://mlsanity.com/paper/2211.06684/) (2022)
- [Balancing Unobserved Confounding with a Few Unbiased Ratings in Debiased Recommendations](https://mlsanity.com/paper/2304.09085/) (2023)
- [Entire Space Counterfactual Learning for Reliable Content Recommendations](https://mlsanity.com/paper/2210.11039/) (2022)
- [Multiple Robust Learning for Recommendation](https://mlsanity.com/paper/2207.10796/) (2022)
- [Debiased Recommendation with Noisy Feedback](https://mlsanity.com/paper/2406.17182/) (2024)
- [Doubly Calibrated Estimator for Recommendation on Data Missing Not At Random](https://mlsanity.com/paper/2403.00817/) (2024)
- [Proximity Matters: Local Proximity Enhanced Balancing for Treatment Effect Estimation](https://mlsanity.com/paper/2407.01111/) (2024)
- [FedAds: A Benchmark for Privacy-Preserving CVR Estimation with Vertical Federated Learning](https://mlsanity.com/paper/2305.08328/) (2023)
- [Debiased Collaborative Filtering with Kernel-Based Causal Balancing](https://mlsanity.com/paper/2404.19596/) (2024)
- [RMT-Net: Reject-aware Multi-Task Network for Modeling Missing-not-at-random Data in Financial Credit Scoring](https://mlsanity.com/paper/2206.00568/) (2022)
- [Robust Graph Clustering via Meta Weighting for Noisy Graphs](https://mlsanity.com/paper/2311.00322/) (2023)
- [Fine-Grained Dynamic Framework for Bias-Variance Joint Optimization on Data Missing Not at Random](https://mlsanity.com/paper/2405.15403/) (2024)
- [Pareto Invariant Representation Learning for Multimedia Recommendation](https://mlsanity.com/paper/2308.04706/) (2023)
- [Entire-Space Variational Information Exploitation for Post-Click Conversion Rate Prediction](https://mlsanity.com/paper/2502.15687/) (2024)
- [Uncertainty Calibration for Counterfactual Propensity Estimation in Recommendation](https://mlsanity.com/paper/2303.12973/) (2023)
- [Deep Stable Multi-Interest Learning for Out-of-distribution Sequential Recommendation](https://mlsanity.com/paper/2304.05615/) (2023)
- [Contrastive Learning for Conversion Rate Prediction](https://mlsanity.com/paper/2307.05974/) (2023)
- [CDR: Conservative Doubly Robust Learning for Debiased Recommendation](https://mlsanity.com/paper/2308.08461/) (2023)
- [Be Aware of the Neighborhood Effect: Modeling Selection Bias under Interference](https://mlsanity.com/paper/2404.19620/) (2024)
- [Exploring and Exploiting Data Heterogeneity in Recommendation](https://mlsanity.com/paper/2305.15431/) (2023)
- [Reconsidering Learning Objectives in Unbiased Recommendation with Unobserved Confounders](https://mlsanity.com/paper/2206.03851/) (2022)
- [Adaptive Pattern Extraction Multi-Task Learning for Multi-Step Conversion Estimations](https://mlsanity.com/paper/2301.02494/) (2023)
- [Addressing Correlated Latent Exogenous Variables in Debiased Recommender Systems](https://mlsanity.com/paper/2506.07517/) (2025)
- [BPL: Bias-adaptive Preference Distillation Learning for Recommender System](https://mlsanity.com/paper/2510.16076/) (2025)

## Abstract (arXiv)

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.