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

Abstract:

This paper introduces an online, distribution-free methodology for managing Conditional Value-at-Risk (CVaR), effectively extending conformal tail risk control mechanisms to environments that are non-stationary and subject to adversarial conditions. In contrast to traditional risk control techniques that depend on the linearity of expectation or data stationarity, our framework delivers rigorous safety assurances for this nonlinear tail risk functional, regardless of arbitrary data-generating processes that may exhibit strategic shifts or drifts over time.

By exploiting the intrinsic links between conformal tail risk control, online learning theory, and the variational representation of CVaR as defined by Rockafellar and Uryasev, we devise a new procedure for online CVaR management that offers guarantees against adversarial regret. Because this method functions without imposing assumptions on the underlying data-generating process, it is widely applicable to contemporary high-stakes deployment scenarios. We establish that the realized empirical CVaR is asymptotically regulated at the specified target level, with the control being asymptotically tight apart from a conservatism gap inherent to finite samples. The efficacy of our approach is validated through applications in portfolio risk management and the mitigation of toxicity in Large Language Models (LLMs), contexts where rare yet catastrophic failures constitute the primary source of systemic risk.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC