Entropy-dial invariance of the Safety Sandwich

Determine whether the Safety Sandwich remains valid when Shannon entropy in the belief-dependent ambiguity radius is replaced by another concave information measure, such as Rényi or Tsallis entropy, provided that the replacement measure vanishes at point-mass beliefs.

Background

RATTL defines its Wasserstein ambiguity radius as proportional to the Shannon entropy of the Bayesian belief. This choice yields a radius that is largest for diffuse beliefs and vanishes as the belief becomes concentrated, supporting the paper’s safety and convergence results.

The authors explicitly propose investigating whether the same value bounds—the worst-case floor and Bayesian best-response ceiling—survive under alternative entropy-like uncertainty measures. The question is restricted to concave measures that are zero at point-mass beliefs, such as Rényi or Tsallis entropy.

References

(iii) R\'enyi/Tsallis entropy as alternative dials---does the Safety Sandwich survive for any concave, zero-at-point-mass information measure?

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