{
  "abstract": "We study hybrid online learning with stochastic features and adversarial labels when the feature distribution is unknown. Prior work gave stochastic sequential covers of log-size $O(d\\log^2 T)$ for a general VC class and logarithmic bounds only under stronger star-type structure. We show that finite VC dimension alone is enough: every binary class of VC dimension $d$ admits a distribution-blind exact cover with log-size $O(d\\log T+\\log(1/δ))$, matching the worst-case $Ω(d\\log(T/d))$ dependence on the horizon. The key ingredient is a new local cube weight that counts Boolean subcubes incident to each realizable trace. Unlike the equal splits used in earlier constructions, we split mass unevenly according to these cube weights; a coordinate-deletion inequality shows that VC dimension controls the total cost of these splits. This yields, to our knowledge, the first tight $O((d+1)\\log T)$ expected worst-case log-loss regret for general VC partitions with unknown i.i.d. features, and an exact polynomial-time implementation for planar affine halfspaces. We also show that the binary phenomenon does not extend from VC dimension to pseudo-dimension: a fixed pseudo-dimension-one sigmoid class requires $Ω(\\log^2 T)$ bits for uniform sequential approximation at accuracy $1/T$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00788",
  "author_total": 2,
  "authors": [
    {
      "name": "Changlong Wu"
    },
    {
      "name": "Wojciech Szpankowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bb7zentjf4wgg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00788",
  "fulltext_url": null,
  "id": "bb7zentjf4wgg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00788",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bb7zentjf4wgg.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:21Z",
      "native_id": "2611.00788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Tight Stochastic Sequential Covers for General VC Classes with Unknown i.i.d. Features",
  "title_text": "Tight Stochastic Sequential Covers for General VC Classes with Unknown i.i.d. Features",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/bb7zentjf4wgg",
  "venue": "arXiv",
  "versions": []
}