From Local Leakage to Global Privacy Risk in Sequential Multi-Agent 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 compositional privacy leakage in sequential LLM agent pipelines. We formalize leakage using mutual information and derive a compositional upper bound relating agent-local leakage to final-output privacy risk 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.