{
  "abstract": "Random features provide a standard approach to scaling kernel methods to large datasets by approximating the kernel with a finite-dimensional feature map. Existing works of random feature methods primarily focus on well-specified models and light-tailed noise conditions, leaving a gap in understanding their performance under more general conditions, such as misspecified models and heavy-tailed noise. In this paper, we provide a comprehensive and improved analysis of kernel ridge regression with random features (KRR-RF) under general conditions. In the light-tailed noise setting, we improve upon the worst-case uniform bounds of the feature map used in the previous works and lead to the minimax optimal learning rates with $2r+γ>α_0$, where $(r,γ,α_0)$ denote the regularity of the target function, the effective dimension of the kernel, and the embedding index of the RKHS, respectively. In the heavy-tailed noise setting, we leverage a recently developed Hilbert-valued Fuk-Nagaev inequality and extend the same optimal results under finite weak moment conditions. The additional cost to achieve robustness is a mildly stronger explicit sample-size requirement than in the light-tailed case. For both settings, our results recover the conditions random features budgets (up to log factors) required in the previous works. In the most benign case when $α_0=γ$, KRR-RF are minimax optimal for all $r \\in (0,1]$. To the best of our knowledge, this is the first work to establish optimal learning rates for KRR-RF under weak moment conditions in the misspecified setting. Numerical experiments and a real data analysis validate the derived learning rates and demonstrate their practical relevance in the presence of mis-specification and heavy-tailed noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18333",
  "author_total": 1,
  "authors": [
    {
      "name": "Caixing Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38r67bbdxzhr3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18333",
  "fulltext_url": null,
  "id": "38r67bbdxzhr3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18333",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7221823478",
  "pdf_url": "https://arxiv.org/pdf/2610.18333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38r67bbdxzhr3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.18333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18333"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "On the Optimality of Random Features under General Conditions: Misspecified Cases and Robust Learning",
  "title_text": "On the Optimality of Random Features under General Conditions: Misspecified Cases and Robust Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/38r67bbdxzhr3",
  "venue": "arXiv",
  "versions": []
}