Infinitesimal gradient boosting (Dombry and Duchamps, 2021) is defined as the vanishing-learning-rate limit of the popular tree-based gradient boosting algorithm from machine learning. It is characterized as the solution of a nonlinear ordinary differential equation in a infinite-dimensional function space where the infinitesimal boosting operator driving the dynamics depends on the training sample. We consider the asymptotic behavior of the model in the large sample limit and prove its convergence to a deterministic process. This population limit is again characterized by a differential equation that depends on the population distribution. We explore some properties of this population limit: we prove that the dynamics makes the test error decrease and we consider its long time behavior.

翻译：无限小梯度提升（Dombry 和 Duchamps, 2021）被定义为机器学习中流行的基于树的梯度提升算法在学习率趋近于零时的极限形式。其核心特征为无限维函数空间中一个非线性常微分方程的解，其中驱动动态过程的无限小提升算子依赖于训练样本。我们考察了该模型在大样本极限下的渐近行为，并证明其收敛于一个确定性过程。该总体极限同样由依赖于总体分布的微分方程刻画。我们探讨了该总体极限的若干性质：证明了动态过程使测试误差递减，并分析了其长期行为。