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.

翻译：本文提出了一种面向决策依赖机会约束问题的表演性场景优化框架。与经典随机优化不同，我们考虑了决策主动塑造底层数据生成过程的反馈回路。我们将表演性解定义为自洽均衡，并利用角谷不动点定理证明了其存在性。为确保无需显式环境模型即可实现计算可解性，我们提出了一种基于无模型场景的近似的交替方法，在数据生成与优化之间迭代进行。在温和的正则条件下，我们证明了配备对数样本量调度策略的随机不动点迭代几乎必然收敛到唯一的表演性解。通过一个新兴的人工智能安全应用——针对大语言模型越狱部署表演性护栏，验证了所提出框架的有效性。数值结果证实了护栏分类器与诱导的对抗提示分布会共同演化并收敛到稳定均衡状态。