# On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control

arXiv: https://arxiv.org/abs/2306.01914 · HTML: https://mlsanity.com/paper/2306.01914/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [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)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [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)
- [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)

## Built on by (most cited first, 3 of 3)

- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [Approximate Model Predictive Control for Microgrid Energy Management via Imitation Learning](https://mlsanity.com/paper/2510.20040/) (2025)
- [Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control](https://mlsanity.com/paper/2410.00859/) (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. At the crux of this theoretical guarantee on smoothness is a new lower bound we prove on the optimality gap of the analytic center associated with a convex Lipschitz function, which we hope could be of independent interest. We validate our theoretical findings via experiments, demonstrating the merits of our smoothing approach over randomized smoothing.