How much data is sufficient to learn high-performing algorithms?

Algorithms for scientific analysis typically have tunable parameters that significantly influence computational efficiency and solution quality. If a parameter setting leads to strong algorithmic performance on average over a set of typical problem instances, that parameter setting---ideally---will perform well in the future. However, if the set of typical problem instances is small, average performance will not generalize to future performance. This raises the question: how large should this set be? We answer this question for any algorithm satisfying an easy-to-describe, ubiquitous property: its performance is a piecewise-structured function of its parameters. We are the first to provide a unified sample complexity framework for algorithm parameter configuration; prior research followed case-by-case analyses. We present applications from diverse domains, including biology, political science, and economics.