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This repository provides code to accompany NIPS2019 paper Deep Gamblers: Learning to Abstain with Portfolio Theory

The code aims to provide an implementation of the method introduced and only supports vgg16 and vgg16_bn models unless manually modified (it defaults to vgg16_bn).


Conventional deep learning image classification minimizes a cross entropy loss measured between the network prediction and the realistic training data. To evaluate the AI's uncertainty about its own prediction, we give it an additional prediction choice corresponding to abstention, and transform the original prediction problem to a gambling problem. The AI choose some prediction choices to bet on and additionally reserve a portion of its money on the abstention choice, and then the AI is trained to maximize the doubling rate of its money. This idea is inspired by portfolio theory.

The training loss for a labelled data (x,y) is therefore

l(x,y)=-log(o*f(x)_y + f(x)_{m+1})

where o is the reward (payoff) of the prediction on label y, and there are totally m categories to predict. f is the model output and f(x)_{m+1} is its prediction on abstention. f(x) is a distribution satisfying \sum_i f(x)_i = 1

Then, we use the reservation f(x)_{m+1} as a disconfidence score to judge whether a data it predicts on is really trustable or not.


To train models for correct prediction rewards (payoffs) o1, o2, o3 respectively,

python3 --rewards o1 o2 o3 --dataset cifar10/svhn/catsdogs

To evaluate the validation error and test error of the trained models with specified predicition coverages,

python3 --rewards o1 o2 o3 --dataset cifar10/svhn/catsdogs --evaluate --coverage cov1 cov2...

In addition, --save argument can be used to specify a path to save trained models and evluate them, and --pretrain argument specifies how many epochs are used for pretraining with the conventional cross entropy loss. Pretraining is useful in case the learning does not start due to a low o parameter. --epochs defaults to 300. When --dataset is cifar10, --pretrain defaults to 100 if o<6.1 and defaults to 0 otherwise.

This implementation is based on


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