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.

翻译：近期研究建立了一个广义Fano框架，用于在交互式统计决策中推导先验预测（贝叶斯）条件风险价值的下界。本文展示了如何将该框架实例化到具体交互问题中，并从其抽象推论中推导出显式的贝叶斯条件风险价值下界。我们的方法通过平方Hellinger距离比较硬模型与参考模型，并将参考铰链项的下界与两个模型的可区分性界相结合。我们将该方法应用于典型示例（包括高斯臂盗问题），获得了显式界，使得关键问题参数的依赖性变得清晰。这些结果表明，广义Fano贝叶斯条件风险价值框架可作为交互式学习与风险敏感决策的实用下界工具。