Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems

TL;DR

This paper applies a generalized-Fano framework to derive explicit Bayesian CVaR lower bounds in interactive decision problems, demonstrating its practical utility in risk-sensitive learning scenarios.

Contribution

It instantiates the generalized-Fano Bayesian CVaR framework in concrete problems, providing explicit bounds that clarify parameter dependencies.

Findings

Derived explicit Bayesian CVaR lower bounds for Gaussian bandits.

Showed how to compare models using squared Hellinger distance.

Demonstrated the framework's applicability to practical interactive learning.

Abstract

Recent work established a generalized-Fano framework for lower bounding prior-predictive (Bayesian) CVaR in interactive statistical decision making. In this paper, we show how to instantiate that framework in concrete interactive problems and derive explicit Bayesian CVaR lower bounds from its abstract corollaries. Our approach compares a hard model with a reference model using squared Hellinger distance, and combines a lower bound on a reference hinge term with a bound on the distinguishability of the two models. We apply this approach to canonical examples, including Gaussian bandits, and obtain explicit bounds that make the dependence on key problem parameters transparent. These results show how the generalized-Fano Bayesian CVaR framework can be used as a practical lower-bound tool for interactive learning and risk-sensitive decision making.