# Active Learning for Nonlinear System Identification with Guarantees

arXiv: https://arxiv.org/abs/2006.10277 · HTML: https://mlsanity.com/paper/2006.10277/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2020.

## Built on by (most cited first, 30 of 80)

- [Transformers as Algorithms: Generalization and Stability in In-context Learning](https://mlsanity.com/paper/2301.07067/) (2023)
- [Representation Learning for Online and Offline RL in Low-rank MDPs](https://mlsanity.com/paper/2110.04652/) (2021)
- [Pessimistic Bootstrapping for Uncertainty-Driven Offline Reinforcement Learning](https://mlsanity.com/paper/2202.11566/) (2022)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning](https://mlsanity.com/paper/2102.09907/) (2021)
- [From Self-Attention to Markov Models: Unveiling the Dynamics of Generative Transformers](https://mlsanity.com/paper/2402.13512/) (2024)
- [Model-based RL with Optimistic Posterior Sampling: Structural Conditions and Sample Complexity](https://mlsanity.com/paper/2206.07659/) (2022)
- [Optimistic Active Exploration of Dynamical Systems](https://mlsanity.com/paper/2306.12371/) (2023)
- [A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/2209.15634/) (2022)
- [MaxInfoRL: Boosting exploration in reinforcement learning through information gain maximization](https://mlsanity.com/paper/2412.12098/) (2024)
- [ASID: Active Exploration for System Identification in Robotic Manipulation](https://mlsanity.com/paper/2404.12308/) (2024)
- [Single Trajectory Nonparametric Learning of Nonlinear Dynamics](https://mlsanity.com/paper/2202.08311/) (2022)
- [A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learning](https://mlsanity.com/paper/2111.11485/) (2021)
- [Optimal Exploration for Model-Based RL in Nonlinear Systems](https://mlsanity.com/paper/2306.09210/) (2023)
- [Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems](https://mlsanity.com/paper/2105.11558/) (2021)
- [Task-Optimal Exploration in Linear Dynamical Systems](https://mlsanity.com/paper/2102.05214/) (2021)
- [Learning Mixtures of Linear Dynamical Systems](https://mlsanity.com/paper/2201.11211/) (2022)
- [PC-MLP: Model-based Reinforcement Learning with Policy Cover Guided Exploration](https://mlsanity.com/paper/2107.07410/) (2021)
- [Non-Linear Reinforcement Learning in Large Action Spaces: Structural Conditions and Sample-efficiency of Posterior Sampling](https://mlsanity.com/paper/2203.08248/) (2022)
- [Sparsity in Partially Controllable Linear Systems](https://mlsanity.com/paper/2110.06150/) (2021)
- [Smoothed Online Learning for Prediction in Piecewise Affine Systems](https://mlsanity.com/paper/2301.11187/) (2023)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions](https://mlsanity.com/paper/2206.05183/) (2022)
- [Active Learning for Control-Oriented Identification of Nonlinear Systems](https://mlsanity.com/paper/2404.09030/) (2024)
- [Model Predictive Control and Reinforcement Learning: A Unified Framework Based on Dynamic Programming](https://mlsanity.com/paper/2406.00592/) (2024)
- [SOMBRL: Scalable and Optimistic Model-Based RL](https://mlsanity.com/paper/2511.20066/) (2025)
- [LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search](https://mlsanity.com/paper/2606.25039/) (2026)
- [Beyond Optimism: Exploration With Partially Observable Rewards](https://mlsanity.com/paper/2406.13909/) (2024)
- [Learning Linear Dynamics from Bilinear Observations](https://mlsanity.com/paper/2409.16499/) (2024)
- [Koopman Spectrum Nonlinear Regulators and Efficient Online Learning](https://mlsanity.com/paper/2106.15775/) (2021)

## Abstract (arXiv)

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.