Handle heavy-tailed or unbounded loss functions in CRC

Develop finite-sample expectation guarantees for conformal risk control when the per-sample loss may be heavy-tailed or unbounded, identifying assumptions and procedures that ensure control of the expected loss at a target level α in the absence of boundedness.

Background

All main theorems in the paper assume bounded losses, which enables the use of Hoeffding-type concentration and yields explicit finite-sample corrections for selection over a finite grid. This boundedness is central to the expectation control results and the minimax lower bound.

In practice, losses may be heavy-tailed or unbounded. Addressing such settings would require alternative techniques (e.g., variance-sensitive or robust concentration, truncation, or robustification) to maintain expectation control without the bounded-loss assumption.