# Model Predictive Control via On-Policy Imitation Learning

arXiv: https://arxiv.org/abs/2210.09206 · HTML: https://mlsanity.com/paper/2210.09206/

## Key facts

- Cited by 6 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 10 of its 45 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Placed in

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

## Builds on (most cited first, 10 of 10)

- [Provably Efficient Imitation Learning from Observation Alone](https://mlsanity.com/paper/1905.10948/) (2019)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Learning Model Predictive Control for iterative tasks. A Data-Driven Control Framework](https://mlsanity.com/paper/1609.01387/) (2016)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Learning the Linear Quadratic Regulator from Nonlinear Observations](https://mlsanity.com/paper/2010.03799/) (2020)
- [TaSIL: Taylor Series Imitation Learning](https://mlsanity.com/paper/2205.14812/) (2022)
- [Efficient Calibration of Embedded MPC](https://mlsanity.com/paper/1911.13021/) (2019)
- [Embedded Online Optimization for Model Predictive Control at Megahertz Rates](https://mlsanity.com/paper/1303.1090/) (2013)

## Built on by (most cited first, 6 of 6)

- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control](https://mlsanity.com/paper/2306.01914/) (2023)
- [Mapping back and forth between model predictive control and neural networks](https://mlsanity.com/paper/2404.12030/) (2024)
- [Reinforcement Learning Compensated Model Predictive Control for Off-road Driving on Unknown Deformable Terrain](https://mlsanity.com/paper/2408.09253/) (2024)
- [Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control](https://mlsanity.com/paper/2410.00859/) (2024)
- [TamedPUMA: safe and stable imitation learning with geometric fabrics](https://mlsanity.com/paper/2503.17432/) (2025)

## Abstract (arXiv)

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.