# On the Limitations of General Purpose Domain Generalisation Methods

arXiv: https://arxiv.org/abs/2202.00563 · HTML: https://mlsanity.com/paper/2202.00563/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 16 of 16)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Bridging Theory and Algorithm for Domain Adaptation](https://mlsanity.com/paper/1904.05801/) (2019)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [Domain Generalization by Marginal Transfer Learning](https://mlsanity.com/paper/1711.07910/) (2017)
- [Generalizing to unseen domains via distribution matching](https://mlsanity.com/paper/1911.00804/) (2019)
- [Marginal Singularity, and the Benefits of Labels in Covariate-Shift](https://mlsanity.com/paper/1803.01833/) (2018)
- [An Online Learning Approach to Interpolation and Extrapolation in Domain Generalization](https://mlsanity.com/paper/2102.13128/) (2021)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [Why Do Self-Supervised Models Transfer? Investigating the Impact of Invariance on Downstream Tasks](https://mlsanity.com/paper/2111.11398/) (2021)

## Built on by (most cited first, 10 of 10)

- [Predicting Fine-Tuning Performance with Probing](https://mlsanity.com/paper/2210.07352/) (2022)
- [On the Generalization of Handwritten Text Recognition Models](https://mlsanity.com/paper/2411.17332/) (2024)
- [Towards Optimization and Model Selection for Domain Generalization: A Mixup-guided Solution](https://mlsanity.com/paper/2209.00652/) (2022)
- [Is Limited Participant Diversity Impeding EEG-based Machine Learning?](https://mlsanity.com/paper/2503.13497/) (2025)
- [Meta Omnium: A Benchmark for General-Purpose Learning-to-Learn](https://mlsanity.com/paper/2305.07625/) (2023)
- [Beyond Finite Data: Towards Data-free Out-of-distribution Generalization via Extrapolation](https://mlsanity.com/paper/2403.05523/) (2024)
- [Generalizable speech deepfake detection via meta-learned LoRA](https://mlsanity.com/paper/2502.10838/) (2025)
- [Benchmarking Domain Generalization Algorithms in Computational Pathology](https://mlsanity.com/paper/2409.17063/) (2024)
- [Domain Generalization Under Posterior Drift](https://mlsanity.com/paper/2510.04441/) (2025)
- [Adapting Time Series Foundation Models through Data Mixtures](https://mlsanity.com/paper/2603.02840/) (2026)

## Abstract (arXiv)

We investigate the fundamental performance limitations of learning algorithms in several Domain Generalisation (DG) settings. Motivated by the difficulty with which previously proposed methods have in reliably outperforming Empirical Risk Minimisation (ERM), we derive upper bounds on the excess risk of ERM, and lower bounds on the minimax excess risk. Our findings show that in all the DG settings we consider, it is not possible to significantly outperform ERM. Our conclusions are limited not only to the standard covariate shift setting, but also two other settings with additional restrictions on how domains can differ. The first constrains all domains to have a non-trivial bound on pairwise distances, as measured by a broad class of integral probability metrics. The second alternate setting considers a restricted class of DG problems where all domains have the same underlying support. Our analysis also suggests how different strategies can be used to optimise the performance of ERM in each of these DG setting. We also experimentally explore hypotheses suggested by our theoretical analysis.