Learning-Efficient Yet Generalizable Collaborative Filtering for Item Recommendation

The weighted squared loss is a common component in several Collaborative Filtering (CF) algorithms for item recommendation, including the representative implicit Alternating Least Squares (iALS). Despite its widespread use, this loss function lacks a clear connection to ranking objectives such as Discounted Cumulative Gain (DCG), posing a fundamental challenge in explaining the exceptional ranking performance observed in these algorithms. In this work, we make a breakthrough by establishing a connection between squared loss and ranking metrics through a Taylor expansion of the DCG-consistent surrogate loss—softmax loss. We also discover a new surrogate squared loss function, namely Ranking-Generalizable Squared (RG$^2$) loss, and conduct thorough theoretical analyses on the DCG-consistency of the proposed loss function. Later, we present an example of utilizing the RG$^2$ loss with Matrix Factorization (MF), coupled with a generalization upper bound and an ALS optimization algorithm that leverages closed-form solutions over all items. Experimental results over three public datasets demonstrate the effectiveness of the RG$^2$ loss, exhibiting ranking performance on par with, or even surpassing, the softmax loss while achieving faster convergence.