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Regret-Optimal Wasserstein-Robust Linear Regression — arXiv:2610.42109

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.42109
License (as archived): CC0-1.0
Archived: 2026-11-03T05:42:06.984Z
SHA-256 of the archived text: 51eeaf3b254ca2ad8f61f2e08ce58fa339b66fe8f80a37244cb67abe1f1be8b9
Stable URL of this page: https://metraipolis.com/documento/dc_ecb1dfd9671e

How to cite

Regret-Optimal Wasserstein-Robust Linear Regression — arXiv:2610.42109 — arXiv (en), https://arxiv.org/abs/2610.42109 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ecb1dfd9671e (Metraipolis archive dc_ecb1dfd9671e, sha256 51eeaf3b254ca2ad8f61f2e08ce58fa339b66fe8f80a37244cb67abe1f1be8b9)

BibTeX

@misc{dcecb1dfd9671e,
  title = {Regret-Optimal Wasserstein-Robust Linear Regression — arXiv:2610.42109},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.42109},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ecb1dfd9671e; sha256 51eeaf3b254ca2ad8f61f2e08ce58fa339b66fe8f80a37244cb67abe1f1be8b9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.42109. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Distributionally robust optimization (DRO) minimizes worst-case risk under distributional uncertainty, but its decisions can be suboptimal in terms of their excess risk, or regret. We study this gap for multivariate least-squares regression, assuming that the observed source law and unknown target law differ by an adversarial 2-Wasserstein perturbation of size $\varepsilon$. We first identify the asymptotic complexity of robust decision-making in the $\varepsilon \to 0$ limit, characterized by a problem-specific condition number $\kappa$. Here, a wide spectrum of simple algorithms, including DRO, achieve the instance-optimal rate of $O(\kappa \varepsilon^2)$. For fixed $\varepsilon > 0$, we prove that DRO still achieves the minimax rate if the problem has bounded residual effective rank. On the other hand, we identify significant failure modes where DRO is provably suboptimal by dimension-dependent factors. Fortunately, we prove that two alternative procedures, minimax regret optimization (MRO) and spectral-norm regularization (SNR), attain the minimax rate. We derive an exact convex reformulation of MRO and an accelerated proximal algorithm for SNR, along with high-probability finite-sample guarantees. We support these theoretical results with numerical experiments separating the performance of MRO and SNR from DRO.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG); Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2610.42109 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T05:26:26.023Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).