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The First-Order Value of Free Covariates in Budgeted Risk Monitoring — arXiv:2611.00576

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00576
License (as archived): CC0-1.0
Archived: 2026-11-03T10:34:17.603Z
SHA-256 of the archived text: b67e0b19cbb0ae3a3d4e82ff113688a87dbc9c5d226c5bda17cc28eaf14f3693
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How to cite

The First-Order Value of Free Covariates in Budgeted Risk Monitoring — arXiv:2611.00576 — arXiv (en), https://arxiv.org/abs/2611.00576 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9eeefb5b034f (Metraipolis archive dc_9eeefb5b034f, sha256 b67e0b19cbb0ae3a3d4e82ff113688a87dbc9c5d226c5bda17cc28eaf14f3693)

BibTeX

@misc{dc9eeefb5b034f,
  title = {The First-Order Value of Free Covariates in Budgeted Risk Monitoring — arXiv:2611.00576},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00576},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9eeefb5b034f; sha256 b67e0b19cbb0ae3a3d4e82ff113688a87dbc9c5d226c5bda17cc28eaf14f3693},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00576. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A deployed model sees its inputs for free, but checking whether its risk has risen requires costly labels. We study how to spend a label budget so that a risk increase is detected quickly while false alarms stay controlled, including under input shifts that keep the risk below a safety threshold $\tau$. Let $A$ be the false-alarm control scale and $h(r)=\mathrm{kl}(r,\tau)$ the Bernoulli KL divergence between the changed risk $r$ and $\tau$. At label rate $b=c/\log A$, we prove that every rule that chooses requests from its own label history has worst-case (Lorden) delay at least $(1/h(r)+1/c)\log A$ to first order: besides collecting evidence, it must wait for its next label. The bound needs only a label budget on one finite stretch of safe source data and false-alarm control over an initial window; a bound on the average time to false alarm does not suffice. When a harmful change also shifts the inputs, a rule that lets the inputs trigger labeling attains delay $\log A/h(r)$ to first order on a fixed Gaussian model, so free covariates save at least $1/b$ rounds. A hybrid rule adds a label-history fallback for risk changes that leave the inputs unchanged. Synthetic experiments and two ACS tasks, with strengthened label-only baselines, show the predicted pattern. The covariate trigger has a cost: because its budget is calibrated on the source, a benign input shift can make it request nearly every label.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2611.00576 — 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 2026-11-03T10:29:48.705Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).