Doubly Robust Collaborative Targeted Learning for Debiased Recommendations

In recommender systems, the collected data always contains various biases and leads to the challenge of accurate predictions. To address selection bias and confounding bias, the doubly robust (DR) method and its variants show superior performance due to the double robustness property and smaller bias under inaccurate propensity and error imputation models. However, we theoretically show that the variance of the error imputation-based (EIB) method is much smaller than that of DR, although EIB may suffer from a much larger bias. In this paper, we propose a doubly robust targeted learning method that effectively combines the small-bias property of DR and the small-variance property of EIB, by leveraging the targeted maximum likelihood estimation technique. Theoretical analysis shows that the proposed targeted learning is effective in reducing the variance of DR while maintaining double robustness. To further reduce the bias and variance during the training process, we propose a novel collaborative targeted learning approach that decomposes imputed errors into parametric and nonparametric parts and updates them collaboratively, resulting in more accurate predictions. Both theoretical analysis and experiments demonstrate the superiority of the proposed methods compared with existing debiasing methods.