Active Learning for Nonlinear System Identification with Guarantees

2020/06/18 by Horia Mania, Michael I. Jordan, Mania, Horia +3 · 10 citations
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2006.10277

openalex publication_date 2020/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and actions or for systems that can be identified from data generated by i.i.d. random inputs. Nonetheless, many interesting dynamical systems have continuous states and actions and can only be identified through a judicious choice of inputs. Motivated by practical settings, we study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. To estimate such systems in finite time identification methods must explore all directions in feature space. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.

Citations

• Online Least Squares Estimation with Self-Normalized Processes: An Application to Bandit Problems
• Probabilistic roadmaps for path planning in high-dimensional configuration spaces
• Learning Linear Dynamical Systems with Semi-Parametric Least Squares
• Stochastic Gradient Descent Learns State Equations with Nonlinear Activations
• Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems
• Learning nonlinear dynamical systems from a single trajectory

Cited by

• Information theory and discriminative sampling for model discovery
• ARCADE: Adaptive Robot Control with Online Changepoint-Aware Bayesian Dynamics Learning
• A Regularization and Active Learning Method for Identification of Quasi Linear Parameter Varying Systems
• SOMBRL: Scalable and Optimistic Model-Based RL
• High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systems
• Hidden Convexity in Active Learning: A Convexified Online Input Design for ARX Systems
• Online Identification of IT Systems through Active Causal Learning
• Federated Nonlinear System Identification
• Robust Adaptive Discrete-Time Control Barrier Certificate
• Central Limit Theorems for Transition Probabilities of Controlled Markov Chains

Related

• Active Learning for Identification of Linear Dynamical Systems
• Active Learning for Control-Oriented Identification of Nonlinear Systems
• Deep active learning for nonlinear system identification
• Online design of experiments by active learning for nonlinear system identification
• Reinforcement Learning in System Identification