# Meta-Learning Online Control for Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2208.10259 · HTML: https://mlsanity.com/paper/2208.10259/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 18 Aug 2022.

## Builds on (most cited first, 19 of 19)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Frustratingly Simple Few-Shot Object Detection](https://mlsanity.com/paper/2003.06957/) (2020)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [Adaptive Gradient-Based Meta-Learning Methods](https://mlsanity.com/paper/1906.02717/) (2019)
- [Online Meta-Learning](https://mlsanity.com/paper/1902.08438/) (2019)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Continual Learning for Robotics: Definition, Framework, Learning Strategies, Opportunities and Challenges](https://mlsanity.com/paper/1907.00182/) (2019)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Learning Linear-Quadratic Regulators Efficiently with only √T Regret](https://mlsanity.com/paper/1902.06223/) (2019)
- [Provable Guarantees for Gradient-Based Meta-Learning](https://mlsanity.com/paper/1902.10644/) (2019)
- [FLEX: Unifying Evaluation for Few-Shot NLP](https://mlsanity.com/paper/2107.07170/) (2021)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Derivative-free online learning of inverse dynamics models](https://mlsanity.com/paper/1809.05074/) (2018)
- [Personalized Rehabilitation Robotics based on Online Learning Control](https://mlsanity.com/paper/2110.00481/) (2021)

## Built on by (most cited first, 5 of 5)

- [Multi-Task Imitation Learning for Linear Dynamical Systems](https://mlsanity.com/paper/2212.00186/) (2022)
- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Data](https://mlsanity.com/paper/2308.04428/) (2023)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics](https://mlsanity.com/paper/2605.24852/) (2026)

## Abstract (arXiv)

In this paper, we consider the problem of finding a meta-learning online control algorithm that can learn across the tasks when faced with a sequence of N (similar) control tasks. Each task involves controlling a linear dynamical system for a finite horizon of T time steps. The cost function and system noise at each time step are adversarial and unknown to the controller before taking the control action. Meta-learning is a broad approach where the goal is to prescribe an online policy for any new unseen task exploiting the information from other tasks and the similarity between the tasks. We propose a meta-learning online control algorithm for the control setting and characterize its performance by textitmeta-regret, the average cumulative regret across the tasks. We show that when the number of tasks are sufficiently large, our proposed approach achieves a meta-regret that is smaller by a factor D/D* compared to an independent-learning online control algorithm which does not perform learning across the tasks, where D is a problem constant and D* is a scalar that decreases with increase in the similarity between tasks. Thus, when the sequence of tasks are similar the regret of the proposed meta-learning online control is significantly lower than that of the naive approaches without meta-learning. We also present experiment results to demonstrate the superior performance achieved by our meta-learning algorithm.