# Gradual Domain Adaptation via Manifold-Constrained Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2410.14061 · HTML: https://mlsanity.com/paper/2410.14061/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [Are Labels Required for Improving Adversarial Robustness?](https://mlsanity.com/paper/1905.13725/) (2019)
- [Understanding Self-Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2002.11361/) (2020)
- [Gradually Vanishing Bridge for Adversarial Domain Adaptation](https://mlsanity.com/paper/2003.13183/) (2020)
- [Understanding Gradual Domain Adaptation: Improved Analysis, Optimal Path and Beyond](https://mlsanity.com/paper/2204.08200/) (2022)
- [Gradual Domain Adaptation in the Wild:When Intermediate Distributions are Absent](https://mlsanity.com/paper/2106.06080/) (2021)
- [Mapping conditional distributions for domain adaptation under generalized target shift](https://mlsanity.com/paper/2110.15057/) (2021)
- [Gradual Domain Adaptation: Theory and Algorithms](https://mlsanity.com/paper/2310.13852/) (2023)
- [Energy-Based Test Sample Adaptation for Domain Generalization](https://mlsanity.com/paper/2302.11215/) (2023)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)
- [Gradual Domain Adaptation via Self-Training of Auxiliary Models](https://mlsanity.com/paper/2106.09890/) (2021)

## Built on by (most cited first, 3 of 3)

- [Beyond Real Data: Synthetic Data through the Lens of Regularization](https://mlsanity.com/paper/2510.08095/) (2025)
- [SWAT: Sliding Window Adversarial Training for Gradual Domain Adaptation](https://mlsanity.com/paper/2501.19155/) (2025)
- [Autonomous Drift Learning in Data Streams: A Unified Perspective](https://mlsanity.com/paper/2605.01295/) (2026)

## Abstract (arXiv)

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions. In particular, we consider a sequence of T≥2 data distributions P1,ldots,PT undergoing a gradual shift, where each pair of consecutive measures Pi,Pi+1 are close to each other in Wasserstein distance. We have a supervised dataset of size n sampled from P0, while for the subsequent distributions in the sequence, only unlabeled i.i.d. samples are available. Moreover, we assume that all distributions exhibit a known favorable attribute, such as (but not limited to) having intra-class soft/hard margins. In this context, we propose a methodology rooted in Distributionally Robust Optimization (DRO) with an adaptive Wasserstein radius. We theoretically show that this method guarantees the classification error across all Pis can be suitably bounded. Our bounds rely on a newly introduced it compatibility measure, which fully characterizes the error propagation dynamics along the sequence. Specifically, for inadequately constrained distributions, the error can exponentially escalate as we progress through the gradual shifts. Conversely, for appropriately constrained distributions, the error can be demonstrated to be linear or even entirely eradicated. We have substantiated our theoretical findings through several experimental results.