Differential Privacy and Entropy in Distributed Control and Optimization

Speaker: Geir E. Dullerud
Affiliation: University of Illinois

Abstract: Widespread availability of new sensors and real-time user data have heralded significant performance improvements in intelligent automation, large-scale distributed monitoring and control systems. At the same time, concerns are growing about the way these systems collect and make use of privacy-sensitive data obtained from individuals. For instance, smartphones and connected vehicles can detect and report on road congestion conditions more accurately by sharing information, and have been used to develop crowd-sourced congestion aware mapping and routing applications; however, researchers have shown that these applications can be used to follow individual user movements, even with anonymized data, as the inherent structure of location data can lead to deanonymization. Similar benefits and risks arise in two-way coordination between consumer demands and electric power utility companies. For example, on one hand, sharing information can prevent over-provisioning through peak-shaving and reduced energy costs, yet on the other, it exposes individual habits.  In this presentation, we focus on a rigorous study of this tension between privacy and performance, by adopting and generalizing to continuous-state dynamical systems the notion of differential privacy, and in particular e-differential privacy. Differential privacy was originally introduced in the literature on databases, and has proven to be both popular and practical in this context. Informally, a differentially private statistical query on a database ensures that the probability distribution of the output is not sensitive to changes in the private data. Thus, an adversary cannot learn much about the participants by querying the output. In this talk we will consider a class of tracking problems involving autonomous agents in distributed control systems where agents are influenced by the aggregate system state, the constituent subsystems are linear and time-invariant (discrete-time), and mean-squared error is used as the performance metric. We study a spectrum of performance-privacy strategies that agents can use, and propose a mechanism for data sharing that ensures differential privacy for the participants. The idea is based on the well-known Laplace mechanism. Also, we connect this work to state estimation and entropy, and establish a lower-bound on the entropy of any unbiased estimator of the private data from any noise-adding mechanism that gives ε-differential privacy. We show that the mechanism achieving this lower-bound is a randomized mechanism that again uses Laplace noise.

     In the final part of the seminar, we will discuss privacy in distributed optimization involving cloud-based architectures (e.g., used in robotic teams), where processes coordinate through a trusted computer. Unlike the typical setting–where state information is to be kept private–here we are concerned with keeping the objective function of each agent private. The challenge is that the same objective functions are used in every time iteration, so mechanisms based on iid noise are ineffective. To solve this problem, we analyze the propagation of perturbations on objective functions over time, and design a correlated-noise mechanism. We provide a trade-off between the privacy of objective functions and the performance of the resulting cloud-based distributed optimization algorithm, and numerically illustrate our theoretical results via simulation examples.

Biography:  Geir E. Dullerud is the W. Grafton and Lillian B. Wilkins Professor in Mechanical Engineering at the University of Illinois at Urbana-Champaign; he is also a member of the Coordinated Science Laboratory, where he is Director of the Decision and Control Laboratory (21 faculty). He is an Affiliate Professor of both Computer Science, and Electrical and Computer Engineering. He has held visiting positions in Electrical Engineering at KTH, Stockholm (2013), and Aeronautics and Astronautics at Stanford University (2005-2006). Earlier he was on faculty in Applied Mathematics at the University of Waterloo (1996-1998), after being a Research Fellow at the California Institute of Technology (1994-1995) in the Control and Dynamical Systems Department.  He has published two books: “A Course in Robust Control Theory”, Texts in Applied Mathematics, Springer, 2000, and “Control of Uncertain Sampled-data Systems”, Birkhauser 1996. His current areas of research interest include convex optimization in control, cyber-physical system security, cooperative robotics, stochastic simulation, and hybrid dynamical systems. In 1999, he received the CAREER Award from the National Science Foundation and in 2005, the Xerox Faculty Research Award at UIUC. He is a Fellow of both IEEE (2008) and ASME (2011).

For more information, contact Prof. Paulo Tabuada ()

Date(s) - Nov 20, 2017
12:30 pm - 1:30 pm

EE-IV Shannon Room #54-134
420 Westwood Plaza - 5th Flr., Los Angeles CA 90095