arXiv Machine Learning By Pauline Bourigault, Emmanuelle Bourigault

Coverage Cliffs in Off-Policy Quantile Certification

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The paper introduces TailCert, a method for certifying an upper tail quantile of a policy’s performance using logged contextual‑bandit data. It builds a PAC‑Bayes Bernstein lower‑confidence envelope over a threshold grid and all data‑dependent posteriors, returning an atom‑safe upper confidence bound on the selected posterior’s pooled p‑quantile. The authors provide finite‑sample guarantees, analyze sample complexity on a rare‑action class, and demonstrate the method’s effectiveness through simulations.

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