Population risk, for instance, measures the expected distance between the model’s prediction for a given input and the ground truth. This means that a good model will minimize some generalization error, f. The goal of a machine learning model is to produce good predictions for unseen data. Convergence criterion for hyperparameter optimization As a consequence, optimizing the empirical estimate too strenuously may in fact be counterproductive. Our criterion acknowledges the fact that the generalization error, which is the true but unknown optimization objective, does not coincide with the empirical estimate optimized by HPO. Our paper, “ Automatic termination for hyperparameter optimization”, suggests a new principled stopping criterion, which, in our experiments, offered a better trade-off between the time consumption of HPO and the accuracy of the resulting models. For instance, a naive approach consists in terminating HPO if the best found configuration remains unchanged for some subsequent evaluations. Still, at some point the search has to be called off, and researchers have proposed a range of stopping criteria. Usually, canvassing all possible hyperparameter configurations is prohibitively time consuming, so hyperparameter optimization (HPO) algorithms are designed to search the configuration space as efficiently as possible. The gap between the green and orange lines is the estimate of the upper bound on the optimizer's regret, or the distance between the ideal hyperparameter configuration and the best configuration found by the optimization algorithm. An example of Bayesian optimization, in which γ is a set of hyperparameter configurations and f-hat is an empirical estimate of the resulting model error.

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