Quantum Learning Theory Beyond Batch Binary Classification
This work addresses the fundamental problem of understanding quantum advantages in learning theory for researchers in quantum computing and machine learning, but it is incremental as it builds directly on prior findings.
The paper extends previous quantum learning theory results from batch binary classification to batch multiclass learning, online boolean learning, and online multiclass learning, showing that quantum sample complexities match classical ones in these settings.
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.