# Stability-Aware Imitation Learning from Model Predictive Control for Autonomous Vehicle Lateral Control: Exact Q-Loss and a Novel Training Procedure

arXiv: https://arxiv.org/abs/2609.23506 · HTML: https://mlsanity.com/paper/2609.23506/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation-learning end-to-end planners, one of 9 directions in End-to-end autonomous driving.
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Placed in

- End-to-end autonomous driving / [Imitation-learning end-to-end planners](https://mlsanity.com/driving/imitation-learning-end-to-end-planners/)
- Offline RL and imitation learning from data / [Imitation and offline RL for driving](https://mlsanity.com/offlinerl/imitation-and-offline-rl-for-driving/)

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

- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints](https://mlsanity.com/paper/1408.3595/) (2014)
- [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)
- [DropoutDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1709.06166/) (2017)

## Abstract (arXiv)

This paper develops a certified imitation-learning framework for approximating model predictive control (MPC) policies with feedforward neural controllers and validates it on autonomous-vehicle lateral control. An exact finite-horizon Q-loss is constructed by fixing the learner's first steering action in the expert MPC problem and re-optimizing the remaining horizon, thereby measuring its downstream optimal-control consequence rather than only pointwise action mismatch. The neural policy is represented as a linear fractional transformation (LFT) interconnection with activation nonlinearities described by sector integral quadratic constraints (IQCs). Combined with a quadratic Lyapunov condition, this representation yields a differentiable certification margin based on the largest eigenvalue of the Lyapunov-IQC matrix. The margin is enforced during training through a logarithmic barrier, while certified Dataset Aggregation (DAgger) and safe projection keep data-aggregation rollouts within the certified policy set. Experiments on a CAD-referenced autonomous-vehicle platform with AprilTag localization and real-time steering demonstrate the resulting closed-loop performance.