# On Applications of Bootstrap in Continuous Space Reinforcement Learning

arXiv: https://arxiv.org/abs/1903.05803 · HTML: https://mlsanity.com/paper/1903.05803/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2019.

## Built on by (most cited first, 9 of 9)

- [Joint Learning-Based Stabilization of Multiple Unknown Linear Systems](https://mlsanity.com/paper/2201.01387/) (2022)
- [Efficient Algorithms for Learning to Control Bandits with Unobserved Contexts](https://mlsanity.com/paper/2202.00867/) (2022)
- [Bayesian Algorithms Learn to Stabilize Unknown Continuous-Time Systems](https://mlsanity.com/paper/2112.15094/) (2021)
- [Worst-case Performance of Greedy Policies in Bandits with Imperfect Context Observations](https://mlsanity.com/paper/2204.04773/) (2022)
- [CLT and Edgeworth Expansion for m-out-of-n Bootstrap Estimators of The Studentized Median](https://mlsanity.com/paper/2505.11725/) (2025)
- [Reinforcement Learning Policies in Continuous-Time Linear Systems](https://mlsanity.com/paper/2109.07630/) (2021)
- [Regret Analysis of Certainty Equivalence Policies in Continuous-Time Linear-Quadratic Systems](https://mlsanity.com/paper/2206.04434/) (2022)
- [On the Effect of Instability on Learning Continuous-Time Linear Control Systems](https://mlsanity.com/paper/2409.11327/) (2024)
- [Model-based Bootstrap of Controlled Markov Chains](https://mlsanity.com/paper/2605.12410/) (2026)

## Abstract (arXiv)

In decision making problems for continuous state and action spaces, linear dynamical models are widely employed. Specifically, policies for stochastic linear systems subject to quadratic cost functions capture a large number of applications in reinforcement learning. Selected randomized policies have been studied in the literature recently that address the trade-off between identification and control. However, little is known about policies based on bootstrapping observed states and actions. In this work, we show that bootstrap-based policies achieve a square root scaling of regret with respect to time. We also obtain results on the accuracy of learning the model's dynamics. Corroborative numerical analysis that illustrates the technical results is also provided.