2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161057We prove existence and uniqueness of the minimizer for the average geodesic distance to the points of a geodesically convex set on the sphere. This implies a corresponding existence and uniqueness result for an optimal algorithm for halfspace learning, when data and target functions are drawn from the uniform distribution.Machine LearningComputational Geometrytext