Stochastic learning to rank (LTR) is a recent branch in the LTR field that concerns the optimization of probabilistic ranking models. Their probabilistic behavior enables certain ranking qualities that are impossible with deterministic models. For example, they can increase the diversity of displayed documents, increase fairness of exposure over documents, and better balance exploitation and exploration through randomization. A core difficulty in LTR is gradient estimation, for this reason, existing stochastic LTR methods have been limited to differentiable ranking models (e.g., neural networks). This is in stark contrast with the general field of LTR where Gradient Boosted Decision Trees (GBDTs) have long been considered the state-of-the-art. In this work, we address this gap by introducing the first stochastic LTR method for GBDTs. Our main contribution is a novel estimator for the second-order derivatives, i.e., the Hessian matrix, which is a requirement for effective GBDTs. To efficiently compute both the first and second-order derivatives simultaneously, we incorporate our estimator into the existing PL-Rank framework, which was originally designed for first-order derivatives only. Our experimental results indicate that stochastic LTR without the Hessian has extremely poor performance, whilst the performance is competitive with the current state-of-the-art with our estimated Hessian. Thus, through the contribution of our novel Hessian estimation method, we have successfully introduced GBDTs to stochastic LTR.

翻译：随机学习排序（LTR）是排序领域的一个新兴分支，主要关注概率排序模型的优化。其概率特性能够实现确定性模型无法企及的排序质量，例如：增加展示文档的多样性、提升文档曝光公平性，以及通过随机化更好地平衡探索与利用。LTR的核心难点在于梯度估计，因此现有随机LTR方法仅限于可微排序模型（如神经网络）。这与LTR主流领域形成鲜明反差——在该领域中，梯度提升决策树（GBDTs）长期被视为最先进技术。本文通过提出首个面向GBDTs的随机LTR方法弥合这一鸿沟。我们的主要贡献在于提出一种新型二阶导数（即海森矩阵）估计器，这是实现高效GBDTs的必要条件。为同时高效计算一阶与二阶导数，我们将该估计器集成至原有仅支持一阶导数计算的PL-Rank框架中。实验结果表明，未使用海森矩阵的随机LTR性能极差，而采用我们估计的海森矩阵后，性能可与当前最优方法相媲美。通过贡献这一新型海森矩阵估计方法，我们成功将GBDTs引入随机LTR领域。