# Online learning with exponential weights in metric spaces

arXiv: https://arxiv.org/abs/2103.14389 · HTML: https://mlsanity.com/paper/2103.14389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 56 references that are in the map.
- First posted on arXiv 26 Mar 2021.

## Builds on (most cited first, 3 of 3)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Measure contraction properties of Carnot groups](https://mlsanity.com/paper/1510.05960/) (2015)

## Built on by (most cited first, 1 of 1)

- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)

## Abstract (arXiv)

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.