Problem
Research questions and friction points this paper is trying to address.
performative prediction
decision-dependent uncertainty
chance-constrained optimization
feedback loop
AI safety
Performative Scenario Optimization
🤖 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.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
performative prediction
decision-dependent uncertainty
scenario optimization
fixed-point iteration
AI safety
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