Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification

2025-01-07

AI Summary

Neural network-based imitation model predictive control (MPC) suffers from unbounded approximation errors, redundant training data, and difficulty in controller lightweighting. Method: This paper proposes a Lipschitz-constrained neural controller design with explicit error bounds. First, it derives a novel closed-form upper bound on the imitation approximation error for MPC. Second, it leverages Lipschitz continuity to guide targeted sampling in error-sensitive regions and integrates optimization problem sensitivity analysis for adaptive data sparsification. Third, it incorporates robust MPC theory to formally guarantee closed-loop stability. Results: Experiments demonstrate that the proposed method significantly reduces the network’s Lipschitz constant, achieves superior closed-loop behavioral fidelity and improved prediction accuracy in inverted pendulum simulations, requires substantially fewer training samples, and provides stronger theoretical stability guarantees compared to baseline approaches.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Natural Language Processing: Safety and Robustness

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset design to ensure the approximation error remains at chosen limits. We discuss how this method can be used to design a stable neural network controller with performance guarantees employing existing robust model predictive control approaches for data generation. Additionally, we introduce a training adjustment, which is based on the sensitivities of the optimization problem and reduces dataset density requirements based on the derived bounds. We verify that the proposed augmentation results in improvements to the network's predictive capabilities and a reduction of the Lipschitz constant. Moreover, on a simulated inverted pendulum problem, we show that the approach results in a closer match of the closed-loop behavior between the imitation and the original model predictive controller.

Problem

• Neural Network
• MPC Control
• Learning Process Simplification

Innovation

• Neural Network Predictive Control
• Error Constraint in Imitation Learning
• Enhanced Training Strategy for Data Efficiency