# Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference

arXiv: https://arxiv.org/abs/2606.00320 · HTML: https://mlsanity.com/paper/2606.00320/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 13 of 13)

- [RealToxicityPrompts: Evaluating Neural Toxic Degeneration in Language Models](https://mlsanity.com/paper/2009.11462/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Prompt Risk Control: A Rigorous Framework for Responsible Deployment of Large Language Models](https://mlsanity.com/paper/2311.13628/) (2023)
- [Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions](https://mlsanity.com/paper/2212.13629/) (2022)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [Policy Learning under Biased Sample Selection](https://mlsanity.com/paper/2304.11735/) (2023)
- [Conformal Tail Risk Control for Large Language Model Alignment](https://mlsanity.com/paper/2502.20285/) (2025)
- [Distribution-Free Statistical Dispersion Control for Societal Applications](https://mlsanity.com/paper/2309.13786/) (2023)
- [QuEst: Enhancing Estimates of Quantile-Based Distributional Measures Using Model Predictions](https://mlsanity.com/paper/2507.05220/) (2025)

## Built on by (most cited first, 2 of 2)

- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)
- [Robust Risk-Sensitive Reinforcement Learning from Corrupted Human Feedback](https://mlsanity.com/paper/2609.38938/) (2026)

## Abstract (arXiv)

We present an online, distribution-free framework for controlling the Conditional Value-at-Risk (CVaR), extending conformal tail risk control to non-stationary and adversarial environments. Unlike classical risk control methods, which rely on stationarity or linearity of expectation, our approach provides provable safety guarantees for a nonlinear tail risk functional under arbitrary data-generating processes that may drift or shift strategically over time. By leveraging deep connections between conformal tail risk control, online learning, and the variational representation of CVaR introduced by Rockafellar and Uryasev, we develop a novel procedure for online CVaR control with adversarial regret guarantees. The proposed method operates without assumptions on the underlying data-generating process, making it broadly applicable in modern high-stakes deployment settings. We prove that the realized empirical CVaR is asymptotically controlled at the target level, and that the resulting control is asymptotically tight up to a finite-sample conservatism gap. We demonstrate the effectiveness of our approach on portfolio risk management and toxicity mitigation for Large Language Models (LLMs), where rare but catastrophic failures dominate system risk.