Classical algorithm design usually focuses on worst-case inputs. Modern applications, however, often come with historical data, synthetic samples, heuristic advice, or learned predictions that reveal structure in the instances of interest. This tutorial surveys principled ways to use such information in algorithm design.

We focus on two frameworks especially relevant to the learning theory community. Algorithms with predictions incorporate possibly noisy predictive advice to improve performance while maintaining robust fallback guarantees. Data-driven algorithm design uses samples from an application domain to select or tune algorithms from rich candidate classes, with PAC and online learning guarantees.