General transport-CVaR–EVaR comparison

Characterize the general transport-CVaR–EVaR relationship induced by Wasserstein ambiguity sets for state spaces with at least three states, including whether a meaningful comparison or identity can be established beyond the canonical two-point catastrophe.

Background

The paper proves that, on a two-state good-state/catastrophe model, a Wasserstein-robust loss is exactly a Conditional Value-at-Risk (CVaR), with the CVaR tail level determined by the Wasserstein radius and hence by belief entropy. For state spaces with at least three states, however, the worst-case transport may distribute probability mass among several low-value states according to their metric distances, producing what the paper calls a transport-CVaR rather than ordinary CVaR.

The authors also note that the matching Entropic Value-at-Risk (EVaR) level depends on the Wasserstein radius without a closed form. Establishing a general comparison between transport-CVaR and EVaR would extend the exact two-point characterization to richer state spaces and clarify the risk-measure interpretation of Wasserstein ambiguity in RATTL.

References

The general transport-CVaR$\leftrightarrow$EVaR comparison is the headline open problem; Proposition~\ref{prop:cvar} settles the canonical case.

— Quantifying Risk Under Evolving Uncertainty: Belief-Dependent Robustness for Safe Sequential Decision Making  (2608.17574 - Ganguly et al., 18 Aug 2026) in Section 4, immediately after Proposition 4.1; reiterated in Section 6, paragraph “Future work”