# Reinforcement Learning in Hyperbolic Spaces: Models and Experiments

arXiv: https://arxiv.org/abs/2410.09466 · HTML: https://mlsanity.com/paper/2410.09466/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 14 of 14)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Scalable Hyperbolic Recommender Systems](https://mlsanity.com/paper/1902.08648/) (2019)
- [Recent advances in directional statistics](https://mlsanity.com/paper/2005.06889/) (2020)
- [Bingham Policy Parameterization for 3D Rotations in Reinforcement Learning](https://mlsanity.com/paper/2202.03957/) (2022)
- [Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning](https://mlsanity.com/paper/2407.16733/) (2024)
- [Optimal navigability of weighted human brain connectomes in physical space](https://mlsanity.com/paper/2311.10669/) (2023)

## Abstract (arXiv)

We examine five setups where an agent (or two agents) seeks to explore unknown environment without any prior information. Although seemingly very different, all of them can be formalized as Reinforcement Learning (RL) problems in hyperbolic spaces. More precisely, it is natural to endow the action spaces with the hyperbolic metric. We introduce statistical and dynamical models necessary for addressing problems of this kind and implement algorithms based on this framework. Throughout the paper we view RL through the lens of the black-box optimization.