An evolutionary approach to black-box optimization on matrix manifolds?

摘要

Optimization on matrix manifolds is a class of methods for solving matrix optimization problems, subject to constraints which admit the structure of a Riemannian manifold. These problems are intractable for traditional evolutionary algorithms due to the non-Euclidean nature. This paper generalizes the classical technique of covariance matrix adaptation to matrix manifolds, and proposes a manifold evolution strategy named ManES. By exploiting the manifold structure, we turn an originally constrained problem into a sequence of unconstrained ones in the Euclidean subspace. The proposed algorithm is coordinate-free, in the sense that it is independent of the choice of basis and requires no global coordinate system. All genetic operators take the form of matrix transformations and thus are computationally efficient. The algorithm exhibits state-of-the-art performance on four benchmark problems and one real-world application posed on three different kinds of matrix manifolds.

关键词