This paper introduces an iterative algorithm designed to train additive models with favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient descent, applied to the coefficients of a truncated basis expansion of the component functions. We show that the resulting estimator satisfies an oracle inequality that allows for model mispecification. In the well-specified setting, by choosing the learning rate carefully across three distinct stages of training, we prove that its risk is minimax optimal in terms of the dependence on the dimensionality of the data and the size of the training sample.

翻译：本文提出了一种迭代算法，旨在以较低的内存存储和计算需求训练加性模型。该算法可视为随机梯度下降在函数空间中的对应方法，应用于分量函数截断基展开的系数。我们证明了所得估计量满足允许模型错误设定的优化不等式。在模型设定正确的情况下，通过精心选择三个不同训练阶段的学习率，我们证明其风险在数据维度和训练样本规模的影响下达到了极小化最优性。