← Back to Library

Performative Scenario Optimization

Authors: Quanyan Zhu, Zhengye Han

Published: 2026-03-31

arXiv ID: 2603.29982v1

Added to Library: 2026-04-01 03:02 UTC

Red Teaming

πŸ“„ Abstract

This paper introduces a performative scenario optimization framework for decision-dependent chance-constrained problems. Unlike classical stochastic optimization, we account for the feedback loop where decisions actively shape the underlying data-generating process. We define performative solutions as self-consistent equilibria and establish their existence using Kakutani's fixed-point theorem. To ensure computational tractability without requiring an explicit model of the environment, we propose a model-free, scenario-based approximation that alternates between data generation and optimization. Under mild regularity conditions, we prove that a stochastic fixed-point iteration, equipped with a logarithmic sample size schedule, converges almost surely to the unique performative solution. The effectiveness of the proposed framework is demonstrated through an emerging AI safety application: deploying performative guardrails against Large Language Model (LLM) jailbreaks. Numerical results confirm the co-evolution and convergence of the guardrail classifier and the induced adversarial prompt distribution to a stable equilibrium.

πŸ” Key Points

  • Introduces a novel performative scenario optimization framework for decision-dependent chance-constrained problems, accounting for feedback loops between decisions and data-generating processes.
  • Establishes the existence of performative solutions as self-consistent equilibria using Kakutani’s fixed-point theorem.
  • Proposes a model-free, stochastic fixed-point iteration that converges almost surely, with practical guarantees under mild regularity conditions.
  • Demonstrates the applicability of the framework in AI safety, specifically deploying performative guardrails against Large Language Model (LLM) jailbreaks.
  • Provides numerical validation showing the convergence of guardrail classifiers and adversarial prompt distributions toward stable equilibria.

πŸ’‘ Why This Paper Matters

This paper is relevant as it presents a significant advancement in optimization methods for dynamic and uncertain environments, particularly in AI security applications. By developing a framework that adapts to adversarial behavior rather than relying on fixed models, it paves the way for more robust and responsive AI defenses.

🎯 Why It's Interesting for AI Security Researchers

AI security researchers will find this paper particularly interesting as it addresses the complexities of adversarial dynamics in AI systems. The framework enables defenders to adapt their strategies in real-time based on the evolving threat landscape, providing insights into how AI systems can be designed to withstand malicious attacks, which is crucial for the safety and reliability of AI technologies.

πŸ“š Read the Full Paper