提出可计算的贝叶斯风险下界，用于交互式决策中的鲁棒性分析。
Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems
- 用平方Hellinger距离比较模型，结合区分度与参考项下界。
- 在高斯赌博机等场景中导出显式下界，清晰展示参数依赖关系。
- 为风险敏感学习提供实用的理论工具，适合关注鲁棒决策的研究者。
近期工作建立了广义Fano框架，用于在交互式统计决策中对先验预测（贝叶斯）条件风险价值（CVaR）进行下界估计。本文展示了如何将该抽象框架具体应用于典型交互问题，并从其推论中导出明确的贝叶斯CVaR下界。方法通过平方Hellinger距离比较一个困难模型与参考模型，结合参考项的下界与两模型可区分性的上界。我们将此方法应用于经典例证，如高斯赌博机（Gaussian bandits），获得显式的下界表达式，清晰揭示关键问题参数的影响。结果表明，广义Fano贝叶斯CVaR框架可作为交互式学习与风险敏感决策的实用下界工具。
原文摘要 · Abstract (English)
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.
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