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Preventing Model Extraction in Contextual Linear Optimization

Adam N. Elmachtoub, Tianyi Lin, Wenxuan Liu · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29918 · cited by 0 works (OpenAlex) · open-access PDF

Portuguese

Considere um problema de otimização de dados lineares contextuais, onde um sistema de predição e otimização (PTO) retorna decisões ideais sem revelar os vetores de custo usados em seu programa linear subsequente. Nosso foco é em como impedir que os atacantes, que podem enviar consultas de contexto, extraam o modelo de previsão subjacente. Embora o mapa de custo-decisão seja multi-a-um, as observações em contextos podem revelar o modelo de previsão subjacente. Para modelos lineares, fornecemos condições suficientes em que o atacante pode aprender o modelo até a escala positiva apenas observando a decisão. Essas condições motivam um ataque adaptativo que alterna a otimização inversa com a amostragem de limites, ou seja, usando consultas de segurança que levam aos limites de

Machine translation (Meta M2M100); the English original follows.

Abstract

Consider a contextual linear optimization problem, where a predict-then-optimize (PTO) system returns optimal decisions without revealing the cost vectors used in its downstream linear program. Our focus is on how to prevent attackers, who can submit context queries, from extracting the underlying prediction model. Although the cost-to-decision map is many-to-one, observations across contexts can reveal the underlying prediction model. For linear models, we provide sufficient conditions where the attacker can learn the model up to positive scaling by only observing the decision. These conditions motivate an adaptive attack that alternates inverse optimization with boundary sampling, i.e., using context queries leading to decision boundaries of the current attacker model. To prevent extraction, we propose a mechanism that perturbs decisions only when the predicted cost vector is near a decision boundary. We establish a regret bound in terms of the perturbation radius. For the attackers that fit the defended responses as optimal decisions under the evaluation distribution, we also prove a lower bound on expected extraction error. Experiments on synthetic instances and real data quantify the security-performance trade-off of the defense mechanism and illustrate that our defense can increase the extraction error.

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Topics: Regret, Computer science, Context (archaeology), Mathematical optimization, Linear programming, Data mining

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