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.

翻译：我们研究了球面上的黑盒优化问题。基于庞加莱和伯格曼球的双曲（信息）几何，通过严格计算自然搜索梯度，设计了两种信息几何优化流（IGO流）。我们证明，球面上广义Kuramoto振子系综能够计算自然搜索梯度，并在两个流形上实现IGO算法。同时指出了伯格曼球中的自然梯度策略与量子决策之间的关系。