The Elliptical Potential Lemma Revisited

TL;DR

This paper offers a new proof and perspectives on the Elliptical Potential Lemma, enhancing understanding and flexibility for future research in online learning and linear stochastic bandits.

Contribution

It provides a novel proof and interpretation of the Elliptical Potential Lemma, broadening its applicability in online learning theory.

Findings

New proof of the Elliptical Potential Lemma

Enhanced flexibility in potential function selection

Potential for future research in online learning

Abstract

This note proposes a new proof and new perspectives on the so-called Elliptical Potential Lemma. This result is important in online learning, especially for linear stochastic bandits. The original proof of the result, however short and elegant, does not give much flexibility on the type of potentials considered and we believe that this new interpretation can be of interest for future research in this field.