The feedback data of recommender systems are often subject to what was exposed to the users; however, most learning and evaluation methods do not account for the underlying exposure mechanism. We first show in theory that applying supervised learning to detect user preferences may end up with inconsistent results in the absence of exposure information. The counterfactual propensity-weighting approach from causal inference can account for the exposure mechanism; nevertheless, the partial-observation nature of the feedback data can cause identifiability issues. We propose a principled solution by introducing a minimax empirical risk formulation. We show that the relaxation of the dual problem can be converted to an adversarial game between two recommendation models, where the opponent of the candidate model characterizes the underlying exposure mechanism. We provide learning bounds and conduct extensive simulation studies to illustrate and justify the proposed approach over a broad range of recommendation settings, which shed insights on the various benefits of the proposed approach.

The authors give a statement that "the recommendation model is optimized over the worst-case exposure mechanism" but fail to give clear motivation behind the model. Why optimizing with the worst-case exposure is better than optimizing with the expected exposure that is widely adopted by existing methods? It seems that the essential advantage of the proposed method is robust. Uncertainty is not a good motivation as it has been considered by existing methods and can not answer the above question. The proposed method should be compared with existing unbiased recommendation methods (e.g. The difference in terms of solutions and generalization bounds between the paper with [a5][a6] should be discussed.

Reviews were quite borderline, but ultimately slightly on the positive side. Given the borderline scores, a discussion was initiated. The reviewers raised some issues about novelty/comparisons (R1,R3), motivation (R2), missing work (R2,R3), and experimental analysis (R4). Mostly though the reviewers did not consider these to be critical issues. The discussion eventually resulted in some positive movement of the scores/comments and reached a consensus around recommending acceptance.

The feedback data of recommender systems are often subject to what was exposed to the users; however, most learning and evaluation methods do not account for the underlying exposure mechanism. We first show in theory that applying supervised learning to detect user preferences may end up with inconsistent results in the absence of exposure information. The counterfactual propensity-weighting approach from causal inference can account for the exposure mechanism; nevertheless, the partial-observation nature of the feedback data can cause identifiability issues. We propose a principled solution by introducing a minimax empirical risk formulation. We show that the relaxation of the dual problem can be converted to an adversarial game between two recommendation models, where the opponent of the candidate model characterizes the underlying exposure mechanism.