Active Learning for Nonlinear System Identification with Guarantees
This addresses a fundamental challenge in model-based reinforcement learning and control for continuous systems, offering a novel approach with theoretical guarantees.
The paper tackles the problem of identifying nonlinear dynamical systems with continuous states and actions, where sample complexity is not well-understood, and proposes an active learning method that achieves estimation at a parametric rate similar to linear regression.
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.