# Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation

arXiv: https://arxiv.org/abs/2010.05862 · HTML: https://mlsanity.com/paper/2010.05862/

## Key facts

- Cited by 87 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2020.

## Built on by (most cited first, 30 of 87)

- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [A Prototype-Oriented Framework for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2110.12024/) (2021)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances](https://mlsanity.com/paper/2210.09160/) (2022)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [Co-Transport for Class-Incremental Learning](https://mlsanity.com/paper/2107.12654/) (2021)
- [The Monge Gap: A Regularizer to Learn All Transport Maps](https://mlsanity.com/paper/2302.04953/) (2023)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [On Robust Optimal Transport: Computational Complexity and Barycenter Computation](https://mlsanity.com/paper/2102.06857/) (2021)
- [Transport-based Counterfactual Models](https://mlsanity.com/paper/2108.13025/) (2021)
- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
- [Scalable Wasserstein Gradient Flow for Generative Modeling through Unbalanced Optimal Transport](https://mlsanity.com/paper/2402.05443/) (2024)
- [Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfe](https://mlsanity.com/paper/2201.00730/) (2022)
- [A Pseudo-Metric between Probability Distributions based on Depth-Trimmed Regions](https://mlsanity.com/paper/2103.12711/) (2021)
- [On Transportation of Mini-batches: A Hierarchical Approach](https://mlsanity.com/paper/2102.05912/) (2021)
- [Unsupervised Noise Adaptive Speech Enhancement by Discriminator-Constrained Optimal Transport](https://mlsanity.com/paper/2111.06316/) (2021)
- [On Unbalanced Optimal Transport: Gradient Methods, Sparsity and Approximation Error](https://mlsanity.com/paper/2202.03618/) (2022)
- [Neural Optimal Transport with Lagrangian Costs](https://mlsanity.com/paper/2406.00288/) (2024)
- [Alignment Attention by Matching Key and Query Distributions](https://mlsanity.com/paper/2110.12567/) (2021)
- [Meta-Learning with Less Forgetting on Large-Scale Non-Stationary Task Distributions](https://mlsanity.com/paper/2209.01501/) (2022)
- [An Optimal Transport Perspective on Unpaired Image Super-Resolution](https://mlsanity.com/paper/2202.01116/) (2022)
- [Extremal Domain Translation with Neural Optimal Transport](https://mlsanity.com/paper/2301.12874/) (2023)
- [Scalable Unbalanced Sobolev Transport for Measures on a Graph](https://mlsanity.com/paper/2302.12498/) (2023)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Generalized Sobolev Transport for Probability Measures on a Graph](https://mlsanity.com/paper/2402.04516/) (2024)
- [Robust Barycenter Estimation using Semi-Unbalanced Neural Optimal Transport](https://mlsanity.com/paper/2410.03974/) (2024)
- [On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexity](https://mlsanity.com/paper/2108.07992/) (2021)
- [Robust Estimation under the Wasserstein Distance](https://mlsanity.com/paper/2302.01237/) (2023)
- [Light Unbalanced Optimal Transport](https://mlsanity.com/paper/2303.07988/) (2023)
- [Analyzing and Improving Optimal-Transport-based Adversarial Networks](https://mlsanity.com/paper/2310.02611/) (2023)

## Abstract (arXiv)

Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function, every sample, including outliers, is weighed similarly due to the marginal constraints. To remedy this issue, robust formulations of OT with unbalanced marginal constraints have previously been proposed. However, employing these methods in deep learning problems such as GANs and domain adaptation is challenging due to the instability of their dual optimization solvers. In this paper, we resolve these issues by deriving a computationally-efficient dual form of the robust OT optimization that is amenable to modern deep learning applications. We demonstrate the effectiveness of our formulation in two applications of GANs and domain adaptation. Our approach can train state-of-the-art GAN models on noisy datasets corrupted with outlier distributions. In particular, our optimization computes weights for training samples reflecting how difficult it is for those samples to be generated in the model. In domain adaptation, our robust OT formulation leads to improved accuracy compared to the standard adversarial adaptation methods. Our code is available at https://github.com/yogeshbalaji/robustOT.