Title: Automatic Termination for Hyperparameter Optimization. Abstract: Bayesian optimization (BO) is a widely popular approach for the hyperparameter optimization (HPO) of machine learning algorithms. At its core, BO iteratively evaluates promising configurations until a user-defined budget, such as wall-clock time or number of iterations, is exhausted. While the final performance after tuning heavily depends on the provided budget, it is hard to pre-specify an optimal value in advance. In this work, we propose an effective and intuitive termination criterion for BO that automatically stops the procedure if it is sufficiently close to the global optima. Across an extensive range of real-world HPO problems, we show that our termination criterion achieves better test performance compared to existing baselines from the literature, such as stopping when the probability of improvement drops below a fixed threshold. We also provide evidence that these baselines are, compared to our method, highly sensitive to the choices of their own hyperparameters. Additionally, we find that overfitting might occur in the context of HPO, which is arguably an overlooked problem in the literature, and show that our termination criterion mitigates this phenomenon on both small and large datasets.