Coverage Cliffs in Off-Policy Quantile Certification
We study when logged contextual-bandit data can certify an upper tail quantile for a policy selected from the same sample.
ProofPaper ↗
Key points
- We construct a PAC-Bayes Bernstein lower-confidence envelope for the target cumulative distribution function (CDF), simultaneous over a predeclared threshold grid and all data-dependent posteriors.
- The resulting procedure, TailCert, uses the envelope's first crossing of level p to return an atom-safe upper confidence bound on the selected posterior's pooled p-quantile (or inconclusive).
- It can also be used to select a policy under a certified tail constraint.
- On an explicit rare-action class, the required sample size grows linearly with the overlap factor W, logarithmically with policy-search and confidence complexity, and quadratically with the inverse CDF safety margin; the upper and lower bounds agree up to constants in the stated regime.
Sources (1)
- [1]Coverage Cliffs in Off-Policy Quantile CertificationarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 07:08 PM
We study when logged contextual-bandit data can certify an upper tail quantile for a policy selected from the same sample.
We construct a PAC-Bayes Bernstein lower-confidence envelope for the target cumulative distribution function (CDF), simultaneous over a predeclared threshold grid and all data-dependent posteriors.
Extractive summary: sentences quoted from the sources.
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