# Information-Geometric Optimization on Spheres

arXiv: https://arxiv.org/abs/2606.07588 · HTML: https://mlsanity.com/paper/2606.07588/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 9 of 9)

- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Spherical Text Embedding](https://mlsanity.com/paper/1911.01196/) (2019)
- [Hyperbolic Deep Reinforcement Learning](https://mlsanity.com/paper/2210.01542/) (2022)
- [Natural Evolutionary Strategies for Variational Quantum Computation](https://mlsanity.com/paper/2012.00101/) (2020)
- [Bingham Policy Parameterization for 3D Rotations in Reinforcement Learning](https://mlsanity.com/paper/2202.03957/) (2022)
- [A group-theoretic framework for machine learning in hyperbolic spaces](https://mlsanity.com/paper/2501.06934/) (2025)
- [Mean field repulsive Kuramoto models: Phase locking and spatial signs](https://mlsanity.com/paper/1803.02647/) (2018)

## Abstract (arXiv)

We consider the black-box optimization problem on a sphere. Two information-geometric optimization flows (IGO flows) are designed with rigorous calculation of natural search gradients based on hyperbolic (information) geometry of Poincar' e and Bergman balls. We demonstrate that ensembles of generalized Kuramoto oscillators on spheres compute natural search gradients and realize IGO algorithms on both manifolds. The relationship between natural gradient policies in Bergman balls and quantum decision making is pointed out.