# Provably adaptive reinforcement learning in metric spaces

arXiv: https://arxiv.org/abs/2006.10875 · HTML: https://mlsanity.com/paper/2006.10875/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Adaptive Discretization in Online Reinforcement Learning](https://mlsanity.com/paper/2110.15843/) (2021)
- [Managing Temporal Resolution in Continuous Value Estimation: A Fundamental Trade-off](https://mlsanity.com/paper/2212.08949/) (2022)
- [Policy Zooming: Adaptive Discretization-based Infinite-Horizon Average-Reward Reinforcement Learning](https://mlsanity.com/paper/2405.18793/) (2024)
- [Provably Adaptive Average Reward Reinforcement Learning for Metric Spaces](https://mlsanity.com/paper/2410.19919/) (2024)

## Abstract (arXiv)

We study reinforcement learning in continuous state and action spaces endowed with a metric. We provide a refined analysis of a variant of the algorithm of Sinclair, Banerjee, and Yu (2019) and show that its regret scales with the zooming dimension of the instance. This parameter, which originates in the bandit literature, captures the size of the subsets of near optimal actions and is always smaller than the covering dimension used in previous analyses. As such, our results are the first provably adaptive guarantees for reinforcement learning in metric spaces.