# StableDR: Stabilized Doubly Robust Learning for Recommendation on Data Missing Not at Random

arXiv: https://arxiv.org/abs/2205.04701 · HTML: https://mlsanity.com/paper/2205.04701/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 10 May 2022.

## Builds on (most cited first, 17 of 17)

- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (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)
- [Causal Intervention for Leveraging Popularity Bias in Recommendation](https://mlsanity.com/paper/2105.06067/) (2021)
- [Feedback Loop and Bias Amplification in Recommender Systems](https://mlsanity.com/paper/2007.13019/) (2020)
- [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)
- [AutoDebias: Learning to Debias for Recommendation](https://mlsanity.com/paper/2105.04170/) (2021)
- [Unbiased Learning to Rank with Unbiased Propensity Estimation](https://mlsanity.com/paper/1804.05938/) (2018)
- [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)
- [Asymmetric Tri-training for Debiasing Missing-Not-At-Random Explicit Feedback](https://mlsanity.com/paper/1910.01444/) (2019)
- [Enhanced Doubly Robust Learning for Debiasing Post-click Conversion Rate Estimation](https://mlsanity.com/paper/2105.13623/) (2021)
- [On the Opportunity of Causal Learning in Recommendation Systems: Foundation, Estimation, Prediction and Challenges](https://mlsanity.com/paper/2201.06716/) (2022)
- [Unbiased Learning for the Causal Effect of Recommendation](https://mlsanity.com/paper/2008.04563/) (2020)
- [TDR-CL: Targeted Doubly Robust Collaborative Learning for Debiased Recommendations](https://mlsanity.com/paper/2203.10258/) (2022)
- [Propensity score regression for causal inference with treatment heterogeneity](https://mlsanity.com/paper/2109.07722/) (2021)

## Built on by (most cited first, 24 of 24)

- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [An Accurate and Interpretable Framework for Trustworthy Process Monitoring](https://mlsanity.com/paper/2302.10426/) (2023)
- [Balancing Unobserved Confounding with a Few Unbiased Ratings in Debiased Recommendations](https://mlsanity.com/paper/2304.09085/) (2023)
- [Doubly Robust Alignment for Large Language Models](https://mlsanity.com/paper/2506.01183/) (2025)
- [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)
- [CausalRM: Causal-Theoretic Reward Modeling for RLHF from Observational User Feedbacks](https://mlsanity.com/paper/2603.18736/) (2026)
- [Debiased Collaborative Filtering with Kernel-Based Causal Balancing](https://mlsanity.com/paper/2404.19596/) (2024)
- [MetaCoCo: A New Few-Shot Classification Benchmark with Spurious Correlation](https://mlsanity.com/paper/2404.19644/) (2024)
- [To Predict or Not To Predict? Proportionally Masked Autoencoders for Tabular Data Imputation](https://mlsanity.com/paper/2412.19152/) (2024)
- [ConvFormer: Revisiting Transformer for Sequential User Modeling](https://mlsanity.com/paper/2308.02925/) (2023)
- [Pareto Invariant Representation Learning for Multimedia Recommendation](https://mlsanity.com/paper/2308.04706/) (2023)
- [ImplicitRM: Unbiased Reward Modeling from Implicit Preference Data for LLM alignment](https://mlsanity.com/paper/2603.23184/) (2026)
- [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)
- [On the Necessity of World Knowledge for Mitigating Missing Labels in Extreme Classification](https://mlsanity.com/paper/2408.09585/) (2024)
- [Learning Counterfactual Outcomes Under Rank Preservation](https://mlsanity.com/paper/2502.06398/) (2025)
- [Addressing Correlated Latent Exogenous Variables in Debiased Recommender Systems](https://mlsanity.com/paper/2506.07517/) (2025)
- [Counterfactual Reciprocal Recommender Systems for User-to-User Matching](https://mlsanity.com/paper/2508.01867/) (2025)
- [BPL: Bias-adaptive Preference Distillation Learning for Recommender System](https://mlsanity.com/paper/2510.16076/) (2025)
- [Principled Synthetic Data Enables the First Scaling Laws for LLMs in Recommendation](https://mlsanity.com/paper/2602.07298/) (2026)
- [Treatment Effect Estimation with Differentiated Networked Effect on Graph Data](https://mlsanity.com/paper/2605.24358/) (2026)

## Abstract (arXiv)

In recommender systems, users always choose the favorite items to rate, which leads to data missing not at random and poses a great challenge for unbiased evaluation and learning of prediction models. Currently, the doubly robust (DR) methods have been widely studied and demonstrate superior performance. However, in this paper, we show that DR methods are unstable and have unbounded bias, variance, and generalization bounds to extremely small propensities. Moreover, the fact that DR relies more on extrapolation will lead to suboptimal performance. To address the above limitations while retaining double robustness, we propose a stabilized doubly robust (StableDR) learning approach with a weaker reliance on extrapolation. Theoretical analysis shows that StableDR has bounded bias, variance, and generalization error bound simultaneously under inaccurate imputed errors and arbitrarily small propensities. In addition, we propose a novel learning approach for StableDR that updates the imputation, propensity, and prediction models cyclically, achieving more stable and accurate predictions. Extensive experiments show that our approaches significantly outperform the existing methods.