Performative Scenario Optimization

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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.

Subjects:

Computer Science and Game Theory (cs.GT)

Cite as: arXiv:2603.29982 [cs.GT]

(or arXiv:2603.29982v1 [cs.GT] for this version)

https://doi.org/10.48550/arXiv.2603.29982

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Zhengye Han [view email] [v1] Tue, 31 Mar 2026 16:44:17 UTC (237 KB)