  We introduce Conformal Decision Theory, a framework for producing safe
autonomous decisions despite imperfect machine learning predictions. Examples
of such decisions are ubiquitous, from robot planning algorithms that rely on
pedestrian predictions, to calibrating autonomous manufacturing to exhibit high
throughput and low error, to the choice of trusting a nominal policy versus
switching to a safe backup policy at run-time. The decisions produced by our
algorithms are safe in the sense that they come with provable statistical
guarantees of having low risk without any assumptions on the world model
whatsoever; the observations need not be I.I.D. and can even be adversarial.
The theory extends results from conformal prediction to calibrate decisions
directly, without requiring the construction of prediction sets. Experiments
demonstrate the utility of our approach in robot motion planning around humans,
automated stock trading, and robot manufacturing.
