Extended Stochastic Derivative-free Optimization on Riemannian Manifolds

In this work we study the generalization of Stochastic Derivative-Free Optimization (SDFO) algorithms from Euclidean spaces to Riemannian manifolds. In the literature, Riemannian adaptations of SDFO relies on the Riemannian exponential map, which imposes local restrictions. We aim to address this restriction using only the intrinsic geometry of the Riemannian manifold.

We first propose Riemannian SDFO (RSDFO), a generalized framework for adapting SDFO algorithms on Euclidean spaces to Riemannian manifolds. We then propose a novel algorithm — Extended RSDFO, and discuss its convergence behaviour on finite volume Riemann manifolds.

Note: The content now part of the book titled Population-Based Optimization on Riemannian Manifolds, please kindly refer to the Books tab.

Joint work with P. Tino.

Robert Simon Fong and Peter Tino. Extended stochastic derivative-free optimization on Riemannian manifolds. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, GECCO ’19, pages 257–258, New York, NY, USA, 2019. ACM
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