Robust asymmetric recommendation via min-max optimization

Recommender systems with implicit feedback (e.g. clicks and purchases) suffer from two critical limitations: 1) imbalanced labels may mislead the learning process of the conventional models that assign balanced weights to the classes; and 2) outliers with large reconstruction errors may dominate the objective function by the conventional $L-2$-norm loss. To address these issues, we propose a robust asymmetric recommendation model. It integrates cost-sensitive learning with capped unilateral loss into a joint objective function, which can be optimized by an iteratively weighted approach. To reduce the computational cost of low-rank approximation, we exploit the dual characterization of the nuclear norm to derive a min-max optimization problem and design a subgradient algorithm without performing full SVD. Finally, promising empirical results demonstrate the effectiveness of our algorithm on benchmark recommendation datasets.