Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control

TL;DR

This paper introduces a novel barrier MPC approach for designing smooth, stable expert controllers in imitation learning, achieving optimal error-smoothness tradeoffs and validated through experiments.

Contribution

It presents a new method for constructing smoothed expert controllers using barrier MPC with theoretical guarantees and improved bounds on optimality gaps.

Findings

Barrier MPC achieves optimal error-to-smoothness tradeoff.

The improved lower bound on the analytic center enhances theoretical understanding.

Experimental results demonstrate the effectiveness of the smoothing approach.

Abstract

Recent work in imitation learning has shown that having an expert controller that is both suitably smooth and stable enables stronger guarantees on the performance of the learned controller. However, constructing such smoothed expert controllers for arbitrary systems remains challenging, especially in the presence of input and state constraints. As our primary contribution, we show how such a smoothed expert can be designed for a general class of systems using a log-barrier-based relaxation of a standard Model Predictive Control (MPC) optimization problem. Improving upon our previous work, we show that barrier MPC achieves theoretically optimal error-to-smoothness tradeoff along some direction. At the core of this theoretical guarantee on smoothness is an improved lower bound we prove on the optimality gap of the analytic center associated with a convex Lipschitz function, which we believe could be of independent interest. We validate our theoretical findings via experiments, demonstrating the merits of our smoothing approach over randomized smoothing.