Universal generalization guarantees for Wasserstein distributionally robust models
Authors: Tam Le, Jerome Malick
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we establish exact generalization guarantees that cover a wide range of cases, with arbitrary transport costs and parametric loss functions, including deep learning objectives with nonsmooth activations. We complete our analysis with an excess bound on the robust objective and an extension to Wasserstein robust models with entropic regularizations. To avoid using concentration results of Fournier & Guillin (2015) involving a radius scaling as O(1/n 1 d ), we develop a novel optimization-based proof, directly tackling the nonsmoothness of the robust objective function (2) with tools from variational analysis (Clarke, 1990; Rockafellar & Wets, 1998; Aliprantis & Border, 2006). |
| Researcher Affiliation | Academia | Tam Le Jërôme Malick Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK Grenoble, 38000, France |
| Pseudocode | No | The paper describes the main approach and proof techniques in Section 4 'Sketch of the Proof' and in the Appendices, but it does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statement about open-sourcing code or provide links to a code repository. |
| Open Datasets | No | The paper discusses various machine learning scenarios and loss functions (e.g., least-squares regression, logistic regression, k-means, deep learning models) as examples where their theoretical framework applies, but it does not specify any particular publicly available datasets used for empirical evaluation. Therefore, no concrete access information for datasets is provided. |
| Dataset Splits | No | The paper focuses on theoretical guarantees and does not describe any experiments involving specific datasets. Therefore, there is no mention of training/test/validation splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any computational experiments. Thus, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper focuses on theoretical analysis and mathematical proofs. It does not mention any specific software dependencies or their version numbers for implementation. |
| Experiment Setup | No | The paper is purely theoretical, providing generalization guarantees and mathematical analyses. It does not describe any experimental setup, hyperparameters, or training configurations. |