The exponentially weighted average forecaster in geodesic spaces of non-positive curvature
This work addresses a theoretical extension of online learning to non-Euclidean spaces, which is incremental as it adapts existing methods to a new geometric setting.
The paper tackles the problem of prediction with expert advice in geodesic spaces with non-positive curvature by extending the exponentially weighted average forecaster using barycenters, and adapts online-to-batch conversion for applications in aggregation and barycenter estimation.
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.