The paper addresses a core question in off-policy evaluation: can we certify a high-quantile performance guarantee for a policy using only logged contextual-bandit data, when that policy was itself selected from the same data? The authors focus on the upper tail of the reward distribution, a quantity relevant for risk-averse deployment.
To answer this, they construct a PAC-Bayes Bernstein lower-confidence envelope for the target cumulative distribution function. This envelope provides a rigorous, data-dependent bound on the quantile, enabling certification despite the statistical dependencies introduced by selecting the policy from the same logged sample.
The abstract is brief and does not elaborate on the empirical results or the precise nature of the 'coverage cliffs' referenced in the title. As a single source, this summary is limited to the stated approach and motivation; further details would require the full manuscript.