# Instantiating Bayesian CVaR lower bounds in Interactive Decision Making Problems

arXiv: https://arxiv.org/abs/2604.12519 · HTML: https://mlsanity.com/paper/2604.12519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Near-Minimax-Optimal Risk-Sensitive Reinforcement Learning with CVaR](https://mlsanity.com/paper/2302.03201/) (2023)
- [Optimal Thompson Sampling strategies for support-aware CVaR bandits](https://mlsanity.com/paper/2012.05754/) (2020)
- [Provably Efficient Risk-Sensitive Reinforcement Learning: Iterated CVaR and Worst Path](https://mlsanity.com/paper/2206.02678/) (2022)
- [Statistical Learning with Conditional Value at Risk](https://mlsanity.com/paper/2002.05826/) (2020)
- [PAC-Bayesian Bound for the Conditional Value at Risk](https://mlsanity.com/paper/2006.14763/) (2020)
- [High-probability minimax lower bounds](https://mlsanity.com/paper/2406.13447/) (2024)
- [Assouad, Fano, and Le Cam with Interaction: A Unifying Lower Bound Framework and Characterization for Bandit Learnability](https://mlsanity.com/paper/2410.05117/) (2024)
- [On the Dual Representation of Coherent Risk Measures](https://mlsanity.com/paper/1502.06155/) (2015)

## Abstract (arXiv)

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.