  This paper addresses the problem of prediction with expert advice for
outcomes in a geodesic space with non-positive curvature in the sense of
Alexandrov. Via geometric considerations, and in particular the notion of
barycenters, we extend to this setting the definition and analysis of the
classical exponentially weighted average forecaster. We also adapt the
principle of online to batch conversion to this setting. We shortly discuss the
application of these results in the context of aggregation and for the problem
of barycenter estimation.
