Information-Theoretic Privacy Control for Sequential Multi-Agent LLM Systems

Sequential multi-agent large language model (LLM) systems are increasingly deployed in sensitive domains such as healthcare, finance, and enterprise decision-making, where multiple specialized agents collaboratively process a single user request. Although individual agents may satisfy local privacy constraints, sensitive information can still be inferred through sequential composition and intermediate representations. In this work, we study \emph{compositional privacy leakage} in sequential LLM agent pipelines. We formalize leakage using mutual information and derive a theoretical bound that characterizes how locally introduced leakage can amplify across agents under sequential execution. Motivated by this analysis, we propose a privacy-regularized training framework that directly constrains information flow between agent outputs and agent-local sensitive variables. We evaluate our approach across sequential agent pipelines of varying depth on three benchmark datasets, demonstrating stable optimization dynamics and consistent, interpretable privacy-utility trade-offs. Our results show that privacy in agentic LLM systems cannot be guaranteed by local constraints alone and must instead be treated as a system-level property during both training and deployment.