# Semi-supervised Learning based on Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/1702.08848 · HTML: https://mlsanity.com/paper/1702.08848/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2017.

## Built on by (most cited first, 12 of 12)

- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [A Unified Wasserstein Distributional Robustness Framework for Adversarial Training](https://mlsanity.com/paper/2202.13437/) (2022)
- [Stochastic Bias-Reduced Gradient Methods](https://mlsanity.com/paper/2106.09481/) (2021)
- [Flow-based Distributionally Robust Optimization](https://mlsanity.com/paper/2310.19253/) (2023)
- [Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Bandits](https://mlsanity.com/paper/2309.08748/) (2023)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Optimal Transport Model Distributional Robustness](https://mlsanity.com/paper/2306.04178/) (2023)
- [Toward Robust Neural Reconstruction from Sparse Point Sets](https://mlsanity.com/paper/2412.16361/) (2024)
- [Out-Of-Domain Unlabeled Data Improves Generalization](https://mlsanity.com/paper/2310.00027/) (2023)
- [An Inexact Halpern Iteration with Application to Distributionally Robust Optimization](https://mlsanity.com/paper/2402.06033/) (2024)
- [A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimization](https://mlsanity.com/paper/2502.17602/) (2025)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)

## Abstract (arXiv)

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.