StochasticRank: Global Optimization of Scale-Free Discrete Functions

In this paper, we introduce a powerful and efficient framework for the direct optimization of ranking metrics. The problem is ill-posed due to the discrete structure of the loss, and to deal with that, we introduce two important techniques: a stochastic smoothing and a novel gradient estimate based on partial integration. We also address the problem of smoothing bias and present a universal solution for a proper debiasing. To guarantee the global convergence of our method, we adopt a recently proposed Stochastic Gradient Langevin Boosting algorithm. Our algorithm is implemented as a part of the CatBoost gradient boosting library and outperforms the existing approaches on several learning to rank datasets. In addition to ranking metrics, our framework applies to any scale-free discreet loss function.