{
  "abstract": "Safety-critical decision systems often require a downstream optimizer to choose from an unknown feasible set determined by an unobserved label $Y$. Given a context $X$, the goal is to construct a safe subset $D(X)$ contained in the oracle feasible set $A(X,Y)$ with probability at least $1-α$. Existing conformal approaches typically construct a prediction set of the unobserved label $Y$ and retain decisions that are safe for every value in this set. Although valid, this requires a stronger intermediate event than set inclusion. We propose Directed Inclusion Safety Calibration (DISC), a conformal framework that directly controls the probability of this inclusion event by reducing its verification to a scalar critical-inclusion score. Given a pretrained nested family of candidate feasible sets, DISC assigns each labeled observation the smallest nestedness level at which the corresponding subset is contained in $A(X,Y)$, and constructs the safe feasible set using an empirical quantile at test-time. With data exchangeability, this yields a finite-sample, distribution-free inclusion guarantee. Under two practical set families, we show that DISC produces a safe feasible set containing that obtained by the corresponding calibration baseline. We further develop optimization-based score computation and decision-aware procedures for learning subset families. Experiments across continuous and structured decision problems show that DISC achieves the target inclusion guarantee while producing larger feasible regions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24496",
  "author_total": 4,
  "authors": [
    {
      "name": "Yajie Bao"
    },
    {
      "name": "Yinjie Min"
    },
    {
      "name": "Haojie Ren"
    },
    {
      "name": "Changliang Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87f30qhgs5yt7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24496",
  "fulltext_url": null,
  "id": "87f30qhgs5yt7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24496",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "1703|Formal Methods in Verification"
    ]
  ],
  "openalex": "W7214016276",
  "pdf_url": "https://arxiv.org/pdf/2609.24496",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87f30qhgs5yt7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:33Z",
      "native_id": "2609.24496",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24496"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Conformalized Safe Feasible Sets in Uncertain Decision Systems",
  "title_text": "Conformalized Safe Feasible Sets in Uncertain Decision Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/87f30qhgs5yt7",
  "venue": "arXiv",
  "versions": []
}