# Learning to steer with Brownian noise

arXiv: https://arxiv.org/abs/2410.03221 · HTML: https://mlsanity.com/paper/2410.03221/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Logarithmic regret for episodic continuous-time linear-quadratic reinforcement learning over a finite-time horizon](https://mlsanity.com/paper/2006.15316/) (2020)
- [Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls](https://mlsanity.com/paper/2104.09311/) (2021)
- [Exploration-exploitation trade-off for continuous-time episodic reinforcement learning with linear-convex models](https://mlsanity.com/paper/2112.10264/) (2021)
- [Learning to reflect: A unifying approach for data-driven stochastic control strategies](https://mlsanity.com/paper/2104.11496/) (2021)
- [Statistical Learning with Sublinear Regret of Propagator Models](https://mlsanity.com/paper/2301.05157/) (2023)
- [Data-driven rules for multidimensional reflection problems](https://mlsanity.com/paper/2311.06639/) (2023)
- [Data-driven optimal stopping: A pure exploration analysis](https://mlsanity.com/paper/2312.05880/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning Optimal Search Strategies](https://mlsanity.com/paper/2603.02356/) (2026)

## Abstract (arXiv)

This paper considers an ergodic version of the bounded velocity follower problem, assuming that the decision maker lacks knowledge of the underlying system parameters and must learn them while simultaneously controlling. We propose algorithms based on moving empirical averages and develop a framework for integrating statistical methods with stochastic control theory. Our primary result is a logarithmic expected regret rate. To achieve this, we conduct a rigorous analysis of the ergodic convergence rates of the underlying processes and the risks of the considered estimators.