aiqbench analysis
The paper treats monitoring a deployed model's risk as a sequential detection problem with a limited label budget. It proves a first-order lower bound on detection delay for rules that rely only on their own label history, and shows that using input covariates to trigger labeling can cut that delay by at least 1/b rounds under a fixed Gaussian model. Readers should note the trade-off it flags: a benign input shift can cause the covariate trigger to request almost every label, so the gains depend on how well the source calibration holds.
The First-Order Value of Free Covariates in Budgeted Risk Monitoring
arXiv:2611.00576v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2611.00576 [cs.LG]
(or arXiv:2611.00576v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.00576 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 332 words