{
  "abstract": "Although Pollak's minimax formulation is one of the central frameworks in quickest change detection (QCD), the strongest general optimality results available for it are predominantly \\emph{asymptotic}, applying as the average run-length-to-false-alarm constraint, $γ$, tends to infinity. Exact results for finite $γ$ have previously been available only for special models or restricted regimes. This paper addresses the general finite-$γ$ problem over the complete class of randomized, history-dependent stopping rules for i.i.d. change models. The key technical development is a \\emph{survival-process representation} that recasts the optimization of Pollak's minimax criterion over stopping times as an equivalent linear variational optimization over admissible survival processes. Although this formulation is infinite-dimensional, it establishes the existence of an optimizer and provides an exact characterization of the finite-$γ$ Pollak minimax value. This characterization, in turn, provides a principled basis for constructing computable stopping rules whose performance can be made arbitrarily close to the optimum. The resulting rules are driven by a recursively updated weighted likelihood-ratio statistic with generally time-varying injections and boundaries. Importantly, this structure is not imposed a priori: the optimization is carried out over the full class of randomized, history-dependent stopping rules, and the Shiryaev--Roberts form emerges naturally from the solution. In particular, the classical Shiryaev--Roberts recursion arises as the time-homogeneous special case. Finally, under a likelihood-ratio floor condition, the framework yields closed-form exact minimax solutions for a nontrivial class of change models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29491",
  "author_total": 1,
  "authors": [
    {
      "name": "Ali Tajer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4xr11q9d9ngn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29491",
  "fulltext_url": null,
  "id": "4xr11q9d9ngn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29491",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7204868462",
  "pdf_url": "https://arxiv.org/pdf/2608.29491",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4xr11q9d9ngn9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2608.29491",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29491"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Pollak's Minimax Quickest Change Detection: Non-Asymptotic Optimality",
  "title_text": "Pollak's Minimax Quickest Change Detection: Non-Asymptotic Optimality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/4xr11q9d9ngn9",
  "venue": "arXiv",
  "versions": []
}