Machine-learned predictors, although achieving very good results for inputs resembling training data, cannot possibly provide perfect predictions in all situations. Still, decision-making systems that are based on such predictors need not only benefit from good predictions, but should also achieve a decent performance when the predictions are inadequate. In this article, we propose a prediction setup for arbitrary metrical task systems (MTS) (e.g., caching , k -server, and convex body chasing ) and online matching on the line . We utilize results from the theory of online algorithms to show how to make the setup robust. Specifically, for caching, we present an algorithm whose performance, as a function of the prediction error, is exponentially better than what is achievable for general MTS. Finally, we present an empirical evaluation of our methods on real-world datasets, which suggests practicality.