  End-to-end engineering design pipelines, in which designs are evaluated using
concurrently defined optimal controllers, are becoming increasingly common in
practice. To discover designs that perform well even under the misspecification
of system dynamics, such end-to-end pipelines have now begun evaluating designs
with a robust control objective in place of the nominal optimal control setup.
Current approaches of specifying such robust control subproblems, however, rely
on hand specification of perturbations anticipated to be present upon
deployment or margin methods that ignore problem structure, resulting in a lack
of theoretical guarantees and overly conservative empirical performance. We,
instead, propose a novel methodology for LQR systems that leverages conformal
prediction to specify such uncertainty regions in a data-driven fashion. Such
regions have distribution-free coverage guarantees on the true system dynamics,
in turn allowing for a probabilistic characterization of the regret of the
resulting robust controller. We then demonstrate that such a controller can be
efficiently produced via a novel policy gradient method that has convergence
guarantees. We finally demonstrate the superior empirical performance of our
method over alternate robust control specifications in a collection of
engineering control systems, specifically for airfoils and a load-positioning
system.
