Variational Encrypted Model Predictive Control

2026-03-19

AI Summary

This work proposes a novel encrypted model predictive control (MPC) framework that enables efficient and privacy-preserving online inference. By reformulating the MPC problem as a sampling-based estimator, the approach naturally accommodates quadratic cost terms through distributional biasing and requires only encrypted polynomial operations during execution. For the first time, variational principles are integrated into encrypted MPC, eliminating intermediate decryptions and additional communication rounds. A dual parallelization mechanism is introduced to substantially enhance scalability. Theoretical analysis quantifies the impact of cryptographic approximation errors on solution optimality, while numerical simulations demonstrate the method’s computational efficiency and practical viability.

Technology Category

Machine Learning: PrivacySearch and Optimization: Mixed Discrete/Continuous SearchReasoning under Uncertainty: Stochastic Optimization

Application Category

Security and Privacy: Applications of cryptographyUser Modeling, Personalization and Recommendation: User privacy protection in personalized systemsEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We develop a variational encrypted model predictive control (VEMPC) protocol whose online execution relies only on encrypted polynomial operations. The proposed approach reformulates the MPC problem into a sampling-based estimator, in which the computation of the quadratic cost is naturally handled by tilting the sampling distribution, thus reducing online encrypted computation. The resulting protocol requires no additional communication rounds or intermediate decryption, and scales efficiently through two complementary levels of parallelism. We analyze the effect of encryption-induced errors on optimality, and simulation results demonstrate the practical applicability of the proposed method.

Problem

• encrypted model predictive control
• variational methods
• privacy-preserving control
• homomorphic encryption
• optimality under encryption

Innovation

• Variational Encrypted MPC
• Encrypted Polynomial Operations
• Sampling-based Estimator
• Tilted Sampling Distribution
• Privacy-preserving Control