Performative Scenario Optimization

2026-03-31

AI Summary

This work addresses the feedback loop between decisions and data generation in decision-dependent chance-constrained optimization by proposing the first model-free scenario optimization framework that incorporates a performative feedback mechanism. The framework alternates between data generation and optimization to seek a self-consistent equilibrium, and establishes the existence of performative solutions via Kakutani’s fixed-point theorem. An algorithm combining stochastic fixed-point iterations, logarithmically increasing sample scheduling, and scenario approximation is further developed, guaranteeing almost sure convergence. Empirical validation on a large language model jailbreaking defense task demonstrates the method’s effectiveness and practicality, successfully achieving co-evolution and stable convergence between the defensive classifier and the distribution of adversarial prompts.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Sampling/Simulation-based SearchConstraint Satisfaction and Optimization: Constraint Optimization

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systemsUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• performative prediction
• decision-dependent uncertainty
• chance-constrained optimization
• feedback loop
• AI safety

Innovation

• performative prediction
• decision-dependent uncertainty
• scenario optimization
• fixed-point iteration
• AI safety