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Cross-validation is the workhorse of modern applied statistics and machinelearning, as it provides a principled framework for selecting the model thatmaximizes generalization performance. In this paper, we show that thecross-validation risk is differentiable with respect to the hyperparameters andtraining data for many common machine learning algorithms, including logisticregression, elastic-net regression, and support vector machines. Leveragingthis property of differentiability, we propose a cross-validation gradientmethod (CVGM) for hyperparameter optimization. Our method enables efficientoptimization in high-dimensional hyperparameter spaces of the cross-validationrisk, the best surrogate of the true generalization ability of our learningalgorithm.

Optimizing for Generalization in Machine Learning with Cross-Validation Gradients