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LambdaMF: Learning Nonsmooth Ranking Functions in Matrix Factorization Using Lambda

This paper emphasizes optimizing ranking measures in a recommendation problem. Since ranking measures are non-differentiable, previous works have been proposed to deal with this problem via approximations or lower/upper bounding of the loss. However, such mismatch between ranking measures and approximations/bounds can lead to non-optimal ranking results. To solve this problem, we propose to model the gradient of non-differentiable ranking measure based on the idea of virtual gradient, which is called lambda in learning to rank. In addition, noticing the difference between learning to rank and recommendation models, we prove that under certain circumstance the existence of popular items can lead to unlimited norm growing of the latent factors in a matrix factorization model. We further create a novel regularization term to remedy such concern. Finally, we demonstrate that our model, LambdaMF, outperforms several state-of-the-art methods. We further show in experiments that in all cases our model achieves global optimum of normalized discount cumulative gain during training. Detailed implementation and supplementary material can be found at (http://www.csie.ntu.edu.tw/~b00902055/).