# A PAC-Bayes Approach for Controlling Unknown Linear Discrete-time Systems

arXiv: https://arxiv.org/abs/2605.10493 · HTML: https://mlsanity.com/paper/2605.10493/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 7 of 7)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [A PAC-Bayesian Framework for Optimal Control with Stability Guarantees](https://mlsanity.com/paper/2403.17790/) (2024)
- [Learning Latent Representations to Co-Adapt to Humans](https://mlsanity.com/paper/2212.09586/) (2022)
- [Learning Robust Data-based LQG Controllers from Noisy Data](https://mlsanity.com/paper/2305.01417/) (2023)

## Abstract (arXiv)

This paper presents a PAC-Bayes framework for learning controllers for unknown stochastic linear discrete-time systems, where the system parameters are drawn from a fixed but unknown distribution. We derive a data-dependent high probability bound on the performance of any learned (stochastic) controller, and propose novel efficient learning algorithms with theoretical guarantees, which can be implemented for both finite and infinite controller spaces. Compared to prior work, our bound holds for unbounded quadratic cost. In the special case where LQG is optimal, our numerical results suggest that the learned controllers achieve comparable performance to LQG.