Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control

Imitation learning has emerged as a powerful tool in machine learning, enabling agents to learn complex behaviors by imitating expert demonstrations acquired either from a human demonstrator or a policy computed offline [3, 11, 12, 13]. Despite its significant success, imitation learning often suffers from a compounding error problem: Successive evaluations of the approximate policy could accumulate error, resulting in out-of-distribution failures [3]. Recent results in imitation learning [31, 32, 34] have identified smoothness (i.e., Lipschitzness of the derivative of the optimal controller with respect to the initial state) and stability of the expert as two key properties that circumvent this issue, thereby allowing for end-to-end performance guarantees for the final learned controller. In this paper, our focus is on enabling such guarantees when the expert being imitated is a Model Predictive Controller (MPC), a powerful class of control algorithms based on solving an optimization problem over a receding prediction horizon [23]. In some cases, the solution to this multiparametric optimization problem, known as the explicit MPC representation [6], can be pre-computed. For instance, in our setup -- linear systems with polytopic constraints -- the optimal control input is a piecewise affine (and, hence, highly non-smooth) function of the state [6].