# Semi-supervised Learning based on Distributionally Robust Optimization

## TL;DR

This paper introduces a semi-supervised learning method based on distributionally robust optimization with optimal transport, improving generalization by leveraging unlabeled data and providing an efficient stochastic gradient descent implementation.

## Contribution

It presents a novel DRO-based SSL framework that enhances generalization and includes a practical training algorithm, advancing the state-of-the-art in semi-supervised learning.

## Key findings

- Improves generalization error over existing SSL methods.
- Effective implementation via stochastic gradient descent.
- Provides insights into the large sample behavior of the uncertainty region.

## Abstract

We propose a novel method for semi-supervised learning (SSL) based on data-driven distributionally robust optimization (DRO) using optimal transport metrics. Our proposed method enhances generalization error by using the unlabeled data to restrict the support of the worst case distribution in our DRO formulation. We enable the implementation of our DRO formulation by proposing a stochastic gradient descent algorithm which allows to easily implement the training procedure. We demonstrate that our Semi-supervised DRO method is able to improve the generalization error over natural supervised procedures and state-of-the-art SSL estimators. Finally, we include a discussion on the large sample behavior of the optimal uncertainty region in the DRO formulation. Our discussion exposes important aspects such as the role of dimension reduction in SSL.