Deep Gamblers: Learning to Abstain with Portfolio Theory

TL;DR

This paper introduces a novel loss function inspired by portfolio theory for selective classification, enabling neural networks to abstain from uncertain predictions and improve performance at various coverage levels.

Contribution

It proposes a new loss function based on gambling doubling rate, allowing end-to-end training of neural networks for selective classification with minimal inference modifications.

Findings

Effective uncertainty identification on SVHN and CIFAR10

Achieves strong results across different coverage levels

Requires minimal changes to existing model architectures

Abstract

We deal with the \textit{selective classification} problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original $m$-class classification problem to $(m+1)$-class where the $(m+1)$-th class represents the model abstaining from making a prediction due to disconfidence. Inspired by portfolio theory, we propose a loss function for the selective classification problem based on the doubling rate of gambling. Minimizing this loss function corresponds naturally to maximizing the return of a \textit{horse race}, where a player aims to balance between betting on an outcome (making a prediction) when confident and reserving one's winnings (abstaining) when not confident. This loss function allows us to train neural networks and characterize the disconfidence of prediction in an end-to-end fashion. In comparison with previous methods, our method requires almost no modification to the model inference algorithm or model architecture. Experiments show that our method can identify uncertainty in data points, and achieves strong results on SVHN and CIFAR10 at various coverages of the data.