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

2026-05-29

AI Summary

Controlling conditional value-at-risk (CVaR)—a nonlinear tail risk measure—remains challenging in non-stationary and even adversarial environments. This work proposes the first distribution-free online framework that extends conformal inference to adversarial settings, achieving asymptotically exact CVaR control under arbitrary data-generating processes by integrating the variational representation of CVaR with online learning. Theoretical analysis establishes finite-sample conservativeness and asymptotic tightness guarantees. Empirical evaluations on portfolio optimization and toxicity mitigation in large language models demonstrate the method’s effectiveness, consistently attaining target CVaR levels with robustness across diverse scenarios.

Abstract

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.

Problem

• Conditional Value-at-Risk
• adversarial environment
• non-stationary
• tail risk control
• distribution-free

Innovation

• Conditional Value-at-Risk
• Conformal Inference
• Adversarial Robustness
• Online Learning
• Risk Control