# Optimal Online Learning using Potential Functions

arXiv: https://arxiv.org/abs/2106.10717 · HTML: https://mlsanity.com/paper/2106.10717/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 17 references that are in the map.
- First posted on arXiv 20 Jun 2021.

## Abstract (arXiv)

We study a family of potential functions for online learning. We show that if the potential function has strictly positive derivatives of order 1-4 then the min-max optimal strategy for the adversary is Brownian motion. Using that fact we analyze different potential functions and show that the Normal-Hedge potential provides the tightest upper bounds on the cumulative regret of the top ε-percentile.