TITLE: Mixing Deep Learning and Multiple Criteria Optimization: An Application to Distributed Learning with Multiple Datasets 

ABSTRACT: The training phase is the most important stage during the machine learning
process. In the case of labeled data and supervised learning, machine training
consists in minimizing the loss function subject to different constraints. In
an abstract setting, it can be formulated as a multiple criteria optimization
model in which each criterion measures the distance between the output
associated with a specific input and its label. Therefore, the fitting term is
a vector function and its minimization is intended in the Pareto sense. We
provide stability results of the efficient solutions with respect to
perturbations of input and output data. We then extend the same approach to the
case of learning with multiple datasets. The multiple dataset environment is
relevant when reducing the bias due to the choice of a specific training set.
We propose a scalarization approach to implement this model and numerical
experiments in digit classification using MNIST data.
The training phase is the most important stage during the machine learning
process. In the case of labeled data and supervised learning, machine training
consists in minimizing the loss function subject to different constraints. In
an abstract setting, it can be formulated as a multiple criteria optimization
model in which each criterion measures the distance between the output
associated with a specific input and its label. Therefore, the fitting term is
a vector function and its minimization is intended in the Pareto sense. We
provide stability results of the efficient solutions with respect to
perturbations of input and output data. We then extend the same approach to the
case of learning with multiple datasets. The multiple dataset environment is
relevant when reducing the bias due to the choice of a specific training set.
We propose a scalarization approach to implement this model and numerical
experiments in digit classification using MNIST data.
Mixing Deep Learning and Multiple Criteria Optimization: An Application to Distributed Learning with Multiple Datasets
http://arxiv.org/abs/2112.01358v1