Open Problem: Is There an Online Learning Algorithm That Learns Whenever Online Learning Is Possible?

TL;DR

This paper explores whether a universal online learning algorithm can exist that guarantees sublinear mistakes across all sequences where such learning is theoretically possible, and investigates conditions that determine this possibility.

Contribution

It formulates the open problem of universal online learning algorithms and examines conditions that characterize sequences allowing sublinear mistake guarantees.

Findings

Open problem formulation for universal online learning algorithms.

Analysis of conditions determining the existence of such algorithms.

Insights into the relationship between sequence properties and learnability.

Abstract

This open problem asks whether there exists an online learning algorithm for binary classification that guarantees, for all target concepts, to make a sublinear number of mistakes, under only the assumption that the (possibly random) sequence of points X allows that such a learning algorithm can exist for that sequence. As a secondary problem, it also asks whether a specific concise condition completely determines whether a given (possibly random) sequence of points X admits the existence of online learning algorithms guaranteeing a sublinear number of mistakes for all target concepts.