  Commonly used optimization-based control strategies such as model-predictive
and control Lyapunov/barrier function based controllers often enjoy provable
stability, robustness, and safety properties. However, implementing such
approaches requires solving optimization problems online at high-frequencies,
which may not be possible on resource-constrained commodity hardware.
Furthermore, how to extend the safety guarantees of such approaches to systems
that use rich perceptual sensing modalities, such as cameras, remains unclear.
In this paper, we address this gap by treating safe optimization-based control
strategies as experts in an imitation learning problem, and train a learned
policy that can be cheaply evaluated at run-time and that provably satisfies
the same safety guarantees as the expert. In particular, we propose Constrained
Mixing Iterative Learning (CMILe), a novel on-policy robust imitation learning
algorithm that integrates ideas from stochastic mixing iterative learning,
constrained policy optimization, and nonlinear robust control. Our approach
allows us to control errors introduced by both the learning task of imitating
an expert and by the distribution shift inherent to deviating from the original
expert policy. The value of using tools from nonlinear robust control to impose
stability constraints on learned policies is shown through sample-complexity
bounds that are independent of the task time-horizon. We demonstrate the
usefulness of CMILe through extensive experiments, including training a
provably safe perception-based controller using a state-feedback-based expert.
