Secure learning-based MPC via garbled circuit

Encrypted control seeks confidential controller evaluation in cloud-based or networked systems. Many existing approaches build on homomorphic encryption (HE) that allow simple mathematical operations to be carried out on encrypted data. Unfortunately, HE is computationally demanding and many control laws (in particular non-polynomial ones) cannot be efficiently implemented with this technology. We show in this paper that secure two-party computation using garbled circuits provides a powerful alternative to HE for encrypted control. More precisely, we present a novel scheme that allows to efficiently implement (non-polynomial) max-out neural networks with one hidden layer in a secure fashion. These networks are of special interest for control since they allow, in principle, to exactly describe piecewise affine control laws resulting from, e.g., linear model predictive control (MPC). However, exact fits require high-dimensional preactivations of the neurons. Fortunately, we illustrate that even low-dimensional learning-based approximations are sufficiently accurate for linear MPC. In addition, these approximations can be securely evaluated using garbled circuit in less than 100~ms for our numerical example. Hence, our approach opens new opportunities for applying encrypted control.