# Reinforcement Learning with Fast Stabilization in Linear Dynamical Systems

arXiv: https://arxiv.org/abs/2007.12291 · HTML: https://mlsanity.com/paper/2007.12291/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2020.

## Built on by (most cited first, 20 of 20)

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- [Augmented RBMLE-UCB Approach for Adaptive Control of Linear Quadratic Systems](https://mlsanity.com/paper/2201.10542/) (2022)
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- [Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances](https://mlsanity.com/paper/2310.03206/) (2023)
- [On the Hardness of Learning to Stabilize Linear Systems](https://mlsanity.com/paper/2311.11151/) (2023)
- [The Confusing Instance Principle for Online Linear Quadratic Control](https://mlsanity.com/paper/2510.19531/) (2025)
- [Optimistic Online LQR via Intrinsic Rewards](https://mlsanity.com/paper/2603.28938/) (2026)
- [Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputs](https://mlsanity.com/paper/2305.16974/) (2023)
- [Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems](https://mlsanity.com/paper/2412.04157/) (2024)
- [Neural Operator based Reinforcement Learning for Control of first-order PDEs with Spatially-Varying State Delay](https://mlsanity.com/paper/2501.18201/) (2025)

## Abstract (arXiv)

In this work, we study model-based reinforcement learning (RL) in unknown stabilizable linear dynamical systems. When learning a dynamical system, one needs to stabilize the unknown dynamics in order to avoid system blow-ups. We propose an algorithm that certifies fast stabilization of the underlying system by effectively exploring the environment with an improved exploration strategy. We show that the proposed algorithm attains tildeO(√T) regret after T time steps of agent-environment interaction. We also show that the regret of the proposed algorithm has only a polynomial dependence in the problem dimensions, which gives an exponential improvement over the prior methods. Our improved exploration method is simple, yet efficient, and it combines a sophisticated exploration policy in RL with an isotropic exploration strategy to achieve fast stabilization and improved regret. We empirically demonstrate that the proposed algorithm outperforms other popular methods in several adaptive control tasks.