Title: On the Safety of Interpretable Machine Learning: A Maximum Deviation Approach. Abstract: Interpretable and explainable machine learning has seen a recent surge of interest. We posit that safety is a key reason behind the demand for explainability. To explore this relationship, we propose a mathematical formulation for assessing the safety of supervised learning models based on their maximum deviation over a certification set. We then show that for interpretable models including decision trees, rule lists, generalized linear and additive models, the maximum deviation can be computed exactly and efficiently. For tree ensembles, which are not regarded as interpretable, discrete optimization techniques can still provide informative bounds. For a broader class of piecewise Lipschitz functions, we repurpose results from the multi-armed bandit literature to show that interpretability produces tighter (regret) bounds on the maximum deviation compared with black box functions. We perform experiments that quantify the dependence of the maximum deviation on model smoothness and certification set size. The experiments also illustrate how the solutions that maximize deviation can suggest safety risks.