Despite the rich literature on machine learning fairness, relatively little
attention has been paid to remediating complex systems, where the final
prediction is the combination of multiple classifiers and where multiple groups
are present. In this paper, we first show that natural baseline approaches for
improving equal opportunity fairness scale linearly with the product of the
number of remediated groups and the number of remediated prediction labels,
rendering them impractical. We then introduce two simple techniques, called
{\em task-overconditioning} and {\em group-interleaving}, to achieve a constant
scaling in this multi-group multi-label setup. Our experimental results in
academic and real-world environments demonstrate the effectiveness of our
proposal at mitigation within this environment.

本文提出了多组多标签系统中两种简单的技术，任务超条件和组交错，以在改善公平性方面取得常数级别的进展。实验结果表明，这种提议在学术和现实环境中具有很高效的可行性。

构成分类的多组公平性提高的可伸缩解决方案

Towards A Scalable Solution for Improving Multi-Group Fairness in  Compositional Classification

We address the challenge of designing optimal adversarial noise algorithms
for settings where a learner has access to multiple classifiers. We demonstrate
how this problem can be framed as finding strategies at equilibrium in a
two-player, zero-sum game between a learner and an adversary. In doing so, we
illustrate the need for randomization in adversarial attacks. In order to
compute Nash equilibrium, our main technical focus is on the design of best
response oracles that can then be implemented within a Multiplicative Weights
Update framework to boost deterministic perturbations against a set of models
into optimal mixed strategies. We demonstrate the practical effectiveness of
our approach on a series of image classification tasks using both linear
classifiers and deep neural networks.

设计最优敌对噪声算法是一项具有挑战性的任务，本文将其表述为学习器和对手之间的一种两方零和博弈，需要利用最佳响应神经网络生成随机化攻击来计算纳什均衡，本文在多个分类任务中演示了该方法的实际有效性。

针对多个分类器的鲁棒性攻击

Robust Attacks against Multiple Classifiers

Intermediate features at different layers of a deep neural network are known
to be discriminative for visual patterns of different complexities. However,
most existing works ignore such cross-layer heterogeneities when classifying
samples of different complexities. For example, if a training sample has
already been correctly classified at a specific layer with high confidence, we
argue that it is unnecessary to enforce rest layers to classify this sample
correctly and a better strategy is to encourage those layers to focus on other
samples.
In this paper, we propose a layer-wise discriminative learning method to
enhance the discriminative capability of a deep network by allowing its layers
to work collaboratively for classification. Towards this target, we introduce
multiple classifiers on top of multiple layers. Each classifier not only tries
to correctly classify the features from its input layer, but also coordinates
with other classifiers to jointly maximize the final classification
performance. Guided by the other companion classifiers, each classifier learns
to concentrate on certain training examples and boosts the overall performance.
Allowing for end-to-end training, our method can be conveniently embedded into
state-of-the-art deep networks. Experiments with multiple popular deep
networks, including Network in Network, GoogLeNet and VGGNet, on scale-various
object classification benchmarks, including CIFAR100, MNIST and ImageNet, and
scene classification benchmarks, including MIT67, SUN397 and Places205,
demonstrate the effectiveness of our method. In addition, we also analyze the
relationship between the proposed method and classical conditional random
fields models.

本文提出了一种基于层的鉴别性学习方法来增强深度神经网络的鉴别能力，在多个层上引入多个分类器，使它们协同工作进行分类，通过对多个深度网络和基准数据集的实验，证明了该方法的有效性，并分析了该方法和经典条件随机场模型之间的关系。