Min-Cost optimality for arbitrary numbers of classes

Establish that Min-Cost is the best possible deterministic algorithm for the Min-Max Regret problem when the classifier has an arbitrary number of classes.

Background

The paper proves matching upper and lower bounds showing that Min-Cost is optimal among deterministic algorithms for the Min-Max Regret criterion in the special case of binary classifiers. The authors then conjecture that the same optimality result extends to classifiers with any number of classes, but no proof is provided for the general case.

References

This shows that Min-Cost is the best possible deterministic algorithm for the Min-Max Regret problem on 2 classes, and we conjecture that this result holds for an arbitrary number of classes.

— Robust Non-Clairvoyant Scheduling with Classification Models  (2610.01343 - Dugois et al., 1 Oct 2026) in Section 5, subsection “Min-Max Regret”