Doubly Robust Collaborative Targeted Learning for Recommendation on Data Missing Not at Random

In recommender systems, the feedback data received is always missing not at random (MNAR), which poses challenges for accurate rating prediction. To address this issue, many recent studies have been conducted on the doubly robust (DR) method and its variants to reduce bias. However, theoretical analysis shows that the DR method has a relatively large variance, while that of the error imputation-based (EIB) method is smaller. In this paper, we propose {\bf DR-TMLE} that effectively captures the merits of both EIB and DR, by leveraging the targeted maximum likelihood estimation (TMLE) technique. DR-TMLE first obtains an initial EIB estimator and then updates the error imputation model along with the bias-reduced direction. Furthermore, we propose a novel RCT-free collaborative targeted learning algorithm for DR-TMLE, called {\bf DR-TMLE-TL}, which updates the propensity model adaptively to reduce the bias of imputed errors. Both theoretical analysis and experiments demonstrate the advantages of the proposed methods compared with existing debiasing methods.