# Online Learning for Supervisory Switching Control

arXiv: https://arxiv.org/abs/2603.14762 · HTML: https://mlsanity.com/paper/2603.14762/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 13 of 13)

- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [A Tutorial on the Non-Asymptotic Theory of System Identification](https://mlsanity.com/paper/2309.03873/) (2023)
- [A New Approach to Learning Linear Dynamical Systems](https://mlsanity.com/paper/2301.09519/) (2023)
- [Online switching control with stability and regret guarantees](https://mlsanity.com/paper/2301.08445/) (2023)
- [Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2309.14648/) (2023)
- [The Sample Complexity of Online Reinforcement Learning: A Multi-model Perspective](https://mlsanity.com/paper/2501.15910/) (2025)
- [Online Bandit Nonlinear Control with Dynamic Batch Length and Adaptive Learning Rate](https://mlsanity.com/paper/2410.03230/) (2024)
- [A least-square method for non-asymptotic identification in linear switching control](https://mlsanity.com/paper/2404.08120/) (2024)

## Abstract (arXiv)

We study supervisory switching control for partially-observed linear dynamical systems. The objective is to identify and deploy a suitable controller for the unknown system by periodically selecting among a collection of N candidate controllers, some of which may destabilize the underlying system. While classical estimator-based supervisory control guarantees asymptotic stability, it lacks quantitative finite-time performance bounds. Conversely, current non-asymptotic methods in both online learning and system identification require restrictive assumptions that are incompatible in a control setting, such as system stability, which preclude testing potentially unstable controllers. To bridge this gap, we propose a novel, non-asymptotic analysis of supervisory control that adapts multi-armed bandit algorithms to a control-theoretic setting. The proposed data-driven algorithm evaluates candidate controllers via scoring criteria that leverage system observability to isolate the effects of state history, enabling both detection of destabilizing controllers and accurate system identification. We present two algorithmic variants with dimension-free, finite-time guarantees, where each identifies the matching controller in O(N log2 N) steps, while simultaneously achieving finite L2-gain with respect to system disturbances.