Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems

2026-04-14

AI Summary

This study investigates the computability and explicit characterization of lower bounds on Bayesian Conditional Value-at-Risk (CVaR) in interactive decision-making settings. Building upon the generalized Fano framework, the authors instantiate this abstract approach to concrete interactive learning problems—such as Gaussian bandits—for the first time by analyzing the squared Hellinger distance between hard and reference models and integrating lower bounds derived from hinge loss with model distinguishability constraints. The resulting analysis yields an explicit Bayesian CVaR lower bound that clearly quantifies its dependence on key problem parameters. This work not only introduces a novel theoretical tool for risk-sensitive decision-making but also demonstrates the effectiveness and practical relevance of the proposed methodology in canonical scenarios.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationMachine Learning: Bayesian LearningComputer Vision: Learning & Optimization for CV

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Bayesian CVaR
• interactive decision making
• lower bounds
• risk-sensitive decision making
• statistical learning

Innovation

• Bayesian CVaR
• generalized Fano framework
• interactive decision making
• Hellinger distance
• risk-sensitive learning