  In this paper, we introduce a powerful and efficient framework for 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: stochastic smoothing and novel gradient estimate based on partial
integration. We show that classic smoothing approaches may introduce bias and
present a universal solution for a proper debiasing. Importantly, we can
guarantee global convergence of our method by adopting 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 discrete loss
function.
