Ambiguous Online Learning

TL;DR

This paper introduces ambiguous online learning, a new framework where learners can produce multiple labels per prediction, allowing for more flexible correctness criteria and establishing a mistake bound trichotomy for hypothesis classes.

Contribution

It defines ambiguous online learning, connects it to multivalued hypotheses, and characterizes the mistake bounds with a novel trichotomy result.

Findings

Mistake bounds are either constant, square root of N, or linear in N.

The framework generalizes existing online learning models.

It applies to multivalued dynamical systems and recommendation algorithms.

Abstract

We propose a new variant of online learning that we call "ambiguous online learning". In this setting, the learner is allowed to produce multiple predicted labels. Such an "ambiguous prediction" is considered correct when at least one of the labels is correct, and none of the labels are "predictably wrong". The definition of "predictably wrong" comes from a hypothesis class in which hypotheses are also multi-valued. Thus, a prediction is "predictably wrong" if it's not allowed by the (unknown) true hypothesis. In particular, this setting is natural in the context of multivalued dynamical systems, recommendation algorithms and lossless compression. It is also strongly related to so-called "apple tasting". We show that in this setting, there is a trichotomy of mistake bounds: up to logarithmic factors, any hypothesis class has an optimal mistake bound of either Theta(1), Theta(sqrt(N)) or N.