---
title: "The First-Order Value of Free Covariates in Budgeted Risk Monitoring"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.00576v1"
permalink: "https://feed.astralor.com/items/itm_a44670c0a0b60050137cdef0"
published: "2026-10-31T03:05:09.000Z"
score: 56
channel: "tech"
tags: ["安全","RAG","The First-Order Value","Free Covariates","Budgeted Risk Monitoring","Let","Bernoulli","Lorden"]
---

# The First-Order Value of Free Covariates in Budgeted Risk Monitoring

## 速览

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 control…

## 关键点

- 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 $τ$.
- Let $A$ be the false-alarm control scale and $h(r)=\mathrm{kl}(r,τ)$ the Bernoulli KL divergence between the changed risk $r$ and $τ$.

## 全文

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 $τ$. Let $A$ be the false-alarm control scale and $h(r)=\mathrm{kl}(r,τ)$ the Bernoulli KL divergence between the changed risk $r$ and $τ$. 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.

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