Online learning with exponential weights in metric spaces
This work addresses online learning problems for scenarios requiring non-Euclidean data structures, but it is incremental as it builds on existing exponential weights methods.
The paper tackles online learning in metric spaces by extending exponential weights analysis from Euclidean to abstract settings, achieving results based on barycenters and curvature bounds, and adapting online-to-batch conversion for statistical learning.
This paper addresses the problem of online learning in metric spaces using exponential weights. We extend the analysis of the exponentially weighted average forecaster, traditionally studied in a Euclidean settings, to a more abstract framework. Our results rely on the notion of barycenters, a suitable version of Jensen's inequality and a synthetic notion of lower curvature bound in metric spaces known as the measure contraction property. We also adapt the online-to-batch conversion principle to apply our results to a statistical learning framework.