  In this paper, we leverage the rapid advances in imitation learning, a topic
of intense recent focus in the Reinforcement Learning (RL) literature, to
develop new sample complexity results and performance guarantees for
data-driven Model Predictive Control (MPC) for constrained linear systems. In
its simplest form, imitation learning is an approach that tries to learn an
expert policy by querying samples from an expert. Recent approaches to
data-driven MPC have used the simplest form of imitation learning known as
behavior cloning to learn controllers that mimic the performance of MPC by
online sampling of the trajectories of the closed-loop MPC system. Behavior
cloning, however, is a method that is known to be data inefficient and suffer
from distribution shifts. As an alternative, we develop a variant of the
forward training algorithm which is an on-policy imitation learning method
proposed by Ross et al. (2010). Our algorithm uses the structure of constrained
linear MPC, and our analysis uses the properties of the explicit MPC solution
to theoretically bound the number of online MPC trajectories needed to achieve
optimal performance. We validate our results through simulations and show that
the forward training algorithm is indeed superior to behavior cloning when
applied to MPC.
