Pick-To-Learn for Systems and Control: theoretical review with a showcase in reachability analysis

Data-Driven methods have become popular tools for tackling increasingly complex design problems in systems and control. In safety critical settings, deploying these methods requires rigorous safety and performance guarantees. Unfortunately, existing approaches often achieve this requirement at the cost of sacrificing valuable data for testing and calibration, or by restricting the design space, thus leading to suboptimal performances. In this work, we introduce Pick-To-Learn (P2L) for Systems and Control, a framework that builds on recent results in sample compression theory to equip any data-driven control method with safety and performance guarantees. Crucially, P2L enables the use of all available data to jointly synthesize and certify the design, eliminating the need to set aside data for calibration or validation purposes. As a result, P2L delivers designs and certificates that improve the current state of the art. We demonstrate this on existing benchmarks in reachability analysis.