Machine learning techniques have been successful for processing complex information, and thus they have the potential to play an important role in data-driven decision-making and control. However, ensuring the reliability of these methods in feedback systems remains a challenge, since classic statistical and algorithmic guarantees do not always hold.

In this talk, I will provide rigorous guarantees of safety and discovery in dynamical settings relevant to robotics and recommendation systems. I take a perspective based on reachability, to specify which parts of the state space the system avoids (safety) or can be driven to (discovery). For data-driven control, we show finite-sample performance and safety guarantees which highlight relevant properties of the system to be controlled. For recommendation systems, we introduce a novel metric of discovery and show that it can be efficiently computed. In closing, I discuss how the reachability perspective can be used to design social-digital systems with a variety of important values in mind.