# Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control

arXiv: https://arxiv.org/abs/2210.12583 · HTML: https://mlsanity.com/paper/2210.12583/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 101 references that are in the map.
- First posted on arXiv 23 Oct 2022.

## Builds on (most cited first, 30 of 46)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [Deep Visual Foresight for Planning Robot Motion](https://mlsanity.com/paper/1610.00696/) (2016)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [Multi-task Self-Supervised Visual Learning](https://mlsanity.com/paper/1708.07860/) (2017)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [On the Generalization Benefit of Noise in Stochastic Gradient Descent](https://mlsanity.com/paper/2006.15081/) (2020)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [NeuroBEM: Hybrid Aerodynamic Quadrotor Model](https://mlsanity.com/paper/2106.08015/) (2021)
- [Deep Sub-Ensembles for Fast Uncertainty Estimation in Image Classification](https://mlsanity.com/paper/1910.08168/) (2019)
- [Safe Learning of Quadrotor Dynamics Using Barrier Certificates](https://mlsanity.com/paper/1710.05472/) (2017)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Model-Based Meta-Reinforcement Learning for Flight with Suspended Payloads](https://mlsanity.com/paper/2004.11345/) (2020)
- [A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty](https://mlsanity.com/paper/2006.01031/) (2020)
- [Context is Everything: Implicit Identification for Dynamics Adaptation](https://mlsanity.com/paper/2203.05549/) (2022)
- [One-Shot Learning of Manipulation Skills with Online Dynamics Adaptation and Neural Network Priors](https://mlsanity.com/paper/1509.06841/) (2015)
- [A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight](https://mlsanity.com/paper/2109.01365/) (2021)
- [HPIPM: a high-performance quadratic programming framework for model predictive control](https://mlsanity.com/paper/2003.02547/) (2020)
- [Fast Online Adaptation in Robotics through Meta-Learning Embeddings of Simulated Priors](https://mlsanity.com/paper/2003.04663/) (2020)
- [Safe Active Dynamics Learning and Control: A Sequential Exploration-Exploitation Framework](https://mlsanity.com/paper/2008.11700/) (2020)

## Built on by (most cited first, 13 of 13)

- [Generative AI for the Optimization of Next-Generation Wireless Networks: Basics, State-of-the-Art, and Open Challenges](https://mlsanity.com/paper/2405.17454/) (2024)
- [SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotors](https://mlsanity.com/paper/2606.23444/) (2026)
- [Feedback Favors the Generalization of Neural ODEs](https://mlsanity.com/paper/2410.10253/) (2024)
- [DroneDiffusion: Robust Quadrotor Dynamics Learning with Diffusion Models](https://mlsanity.com/paper/2409.11292/) (2024)
- [Constrained Reinforcement Learning using Distributional Representation for Trustworthy Quadrotor UAV Tracking Control](https://mlsanity.com/paper/2302.11694/) (2023)
- [First, Learn What You Don't Know: Active Information Gathering for Driving at the Limits of Handling](https://mlsanity.com/paper/2411.00107/) (2024)
- [Learning Long-Horizon Predictions for Quadrotor Dynamics](https://mlsanity.com/paper/2407.12964/) (2024)
- [NOVA: Navigation via Object-Centric Visual Autonomy for High-Speed Target Tracking in Unstructured GPS-Denied Environments](https://mlsanity.com/paper/2506.18689/) (2025)
- [PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments](https://mlsanity.com/paper/2507.00816/) (2025)
- [Efficient Deep Learning of Robust, Adaptive Policies using Tube MPC-Guided Data Augmentation](https://mlsanity.com/paper/2303.15688/) (2023)
- [Proto-MPC: An Encoder-Prototype-Decoder Approach for Quadrotor Control in Challenging Winds](https://mlsanity.com/paper/2401.15508/) (2024)
- [Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures](https://mlsanity.com/paper/2505.19521/) (2025)
- [Thompson Sampling-Based Learning and Control for Unknown Dynamic Systems](https://mlsanity.com/paper/2506.22186/) (2025)

## Abstract (arXiv)

Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.