  We present a method for learning to satisfy uncertain constraints from
demonstrations. Our method uses robust optimization to obtain a belief over the
potentially infinite set of possible constraints consistent with the
demonstrations, and then uses this belief to plan trajectories that trade off
performance with satisfying the possible constraints. We use these trajectories
in a closed-loop policy that executes and replans using belief updates, which
incorporate data gathered during execution. We derive guarantees on the
accuracy of our constraint belief and probabilistic guarantees on plan safety.
We present results on a 7-DOF arm and 12D quadrotor, showing our method can
learn to satisfy high-dimensional (up to 30D) uncertain constraints, and
outperforms baselines in safety and efficiency.
