# Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control

arXiv: https://arxiv.org/abs/2410.00859 · HTML: https://mlsanity.com/paper/2410.00859/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 12 of 12)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Oracle Complexity in Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2104.06763/) (2021)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior](https://mlsanity.com/paper/2307.14619/) (2023)
- [TaSIL: Taylor Series Imitation Learning](https://mlsanity.com/paper/2205.14812/) (2022)
- [A Neural Network Architecture to Learn Explicit MPC Controllers from Data](https://mlsanity.com/paper/1911.10789/) (2019)
- [Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear Systems](https://mlsanity.com/paper/1503.03314/) (2015)
- [Model Predictive Control via On-Policy Imitation Learning](https://mlsanity.com/paper/2210.09206/) (2022)
- [Short-step Methods Are Not Strongly Polynomial-Time](https://mlsanity.com/paper/2201.02768/) (2022)
- [On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control](https://mlsanity.com/paper/2306.01914/) (2023)
- [Improving the Bit Complexity of Communication for Distributed Convex Optimization](https://mlsanity.com/paper/2403.19146/) (2024)

## Abstract (arXiv)

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.