Machine Learning (ML) models are increasingly used to support or substitute decision making. In applications where skilled experts are a limited resource, it is crucial to reduce their burden and automate decisions when the performance of an ML model is at least of equal quality. However, models are often pre-trained and fixed, while tasks arrive sequentially and their distribution may shift. In that case, the respective performance of the decision makers may change, and the deferral algorithm must remain adaptive. We propose a contextual bandit model of this online decision making problem. Our framework includes budget constraints and different types of partial feedback models. Beyond the theoretical guarantees of our algorithm, we propose efficient extensions that achieve remarkable performance on real-world datasets.