Task-Driven Detection of Distribution Shifts With Statistical Guarantees for Robot Learning

Our goal is to perform <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out-of-distribution (OOD) detection</i>, i.e., to detect when a robot is operating in environments drawn from a different distribution than the ones used to train the robot. We leverage probably approximately correct-Bayes theory to train a policy with a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">guaranteed bound</i> on performance on the training distribution. Our idea for OOD detection relies on the following intuition: violation of the performance bound on test environments provides evidence that the robot is operating OOD. We formalize this via statistical techniques based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula>-values and concentration inequalities. The approach provides guaranteed confidence bounds on OOD detection including bounds on both the false-positive and false-negative rates of the detector and is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">task-driven</i> and only sensitive to changes that impact the robot's performance. We demonstrate our approach in simulation and hardware for a grasping task using objects with unfamiliar shapes or poses and a drone performing vision-based obstacle avoidance in environments with wind disturbances and varied obstacle densities. Our examples demonstrate that we can perform task-driven OOD detection within just a handful of trials.