A stochastic algorithm is proposed, finding the set of generalized meansassociated to a probability measure on a compact Riemannian manifold M and acontinuous cost function on the product of M by itself. Generalized meansinclude p-means for p>0, computed with any continuous distance function, notnecessarily the Riemannian distance. They also include means for lengthscomputed from Finsler metrics, or for divergences. The algorithm is fedsequentially with independent random variables Y_n distributed according to theprobability measure on the manifold and this is the only knowledge of thismeasure required. It evolves like a Brownian motion between the times it jumpsin direction of the Y_n. Its principle is based on simulated annealing andhomogenization, so that temperature and approximations schemes must be tunedup. The proof relies on the investigation of the evolution of atime-inhomogeneous L^2 functional and on the corresponding spectral gapestimates due to Holley, Kusuoka and Stroock.
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