A Framework for Population-Based Stochastic Optimization on Abstract Riemannian Manifolds

Understand

We present Extended Riemannian Stochastic Derivative-Free Optimization (Extended RSDFO), a novel population-based stochastic optimization algorithm on Riemannian manifolds that addresses the locality and implicit assumptions of manifold optimization in the literature.

• We begin by investigating the Information Geometrical structure of statistical model over Riemannian manifolds.
• This establishes a geometrical framework of Extended RSDFO using both the statistical geometry of the decision space and the Riemannian geometry of the search space.
• We construct locally inherited probability distribution via an orientation-preserving diffeomorphic bundle morphism, and then extend the information geometrical structure to mixture densities over totally bounded subsets of manifolds.