Quantum Learning Theory Beyond Batch Binary Classification

TL;DR

This paper extends quantum learning theory beyond batch binary classification to multiclass and online settings, introducing models with quantum examples and analyzing their sample complexities and adversarial scenarios.

Contribution

It introduces the first models of online learning with quantum examples and extends quantum learning complexity results to multiclass and online frameworks.

Findings

Quantum sample complexity matches classical in batch settings.

Extended quantum learning results to multiclass and online learning.

Introduced the first model of online learning with quantum examples.

Abstract

Arunachalam and de Wolf (2018) showed that the sample complexity of quantum batch learning of boolean functions, in the realizable and agnostic settings, has the same form and order as the corresponding classical sample complexities. In this paper, we extend this, ostensibly surprising, message to batch multiclass learning, online boolean learning, and online multiclass learning. For our online learning results, we first consider an adaptive adversary variant of the classical model of Dawid and Tewari (2022). Then, we introduce the first (to the best of our knowledge) model of online learning with quantum examples.