Active Learning for Nonlinear System Identification with Guarantees

TL;DR

This paper introduces an active learning method for identifying nonlinear dynamical systems with guarantees, achieving parametric estimation rates by exploring feature space efficiently.

Contribution

It proposes a novel active learning approach combining trajectory planning, tracking, and re-estimation for nonlinear system identification with theoretical guarantees.

Findings

Achieves parametric rate of system estimation

Effectively explores feature space through active learning

Provides theoretical guarantees for nonlinear system identification

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.