Exact Risk-Complexity Laws for Projective Boundaries in Scenario Optimization and Distribution-Free Certification
Scenario optimization, conformal prediction, and related distribution-free certification methods use finite samples to construct decisions or prediction sets with violation-risk guarantees for fresh observations. In several classical settings, the conditional violation risk follows an exact beta law, whose tail has a beta-binomial representation and whose parameter is a support, calibration, or compression dimension. This paper identifies the deterministic boundary mechanism behind these formulas and derives the corresponding law when the observed boundary size is random. A decision rule is represented by an acceptance set for future observations, together with a boundary map selecting th...
| Authors | Giuseppe C. Calafiore |
|---|---|
| Primary category | eess.SY |
| Published | 1 September 2026 |
| Last updated at source | 1 September 2026 |
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