Online Learning via Sequential Complexities

TL;DR

This paper introduces sequential complexity measures extending classical statistical learning tools to sequential prediction, providing precise learnability conditions and enabling analysis without explicit algorithms.

Contribution

It develops a new theoretical framework of sequential complexities that generalizes classical measures for online learning analysis.

Findings

Provides necessary and sufficient conditions for online learnability.

Establishes learnability results without explicit algorithms.

Extends classical complexity measures to the sequential setting.

Abstract

We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our proposed sequential complexities can be seen as extensions of these measures to the sequential setting. The developed theory is shown to yield precise learning guarantees for the problem of sequential prediction. In particular, we show necessary and sufficient conditions for online learnability in the setting of supervised learning. Several examples show the utility of our framework: we can establish learnability without having to exhibit an explicit online learning algorithm.