Erfan Nozari

Differentially private distributed convex optimization via objective perturbation

This paper studies the problem of differentially private distributed convex unconstrained optimization for multi-agent systems. A group of agents seek to minimize the aggregate sum of their individual objective functions. Each agent only knows its own objective function and wants to keep it private from other agents or eavesdroppers listening to the network communications. Our design strategy consists of perturbing the objective functions with Laplace noise so that any query on the functions or their attributes is differentially private. This, together with the fact that differential privacy is immune to post-processing, allows us to employ any distributed algorithm that solves the unconstrained convex optimization problem on the perturbed objective functions. Our technical approach carefully describes how these perturbations can be selected so that the resulting functions retain the requirements on smoothness and convexity critical to many optimization algorithms. We quantify the magnitude of the expected deviation of the algorithm output from the true optimizer. The specific choice of distributed optimization algorithm determines the requirements on the network communication graph. Simulations illustrate the strengths of the proposed approach.

Differentially Private Distributed Convex Optimization via Functional Perturbation

We study a class of distributed convex constrained optimization problems where a group of agents aim to minimize the sum of individual objective functions while each desires that any information about its objective function is kept private. We prove the impossibility of achieving differential privacy using strategies based on perturbing the inter-agent messages with noise when the underlying noise-free dynamics are asymptotically stable. This justifies our algorithmic solution based on the perturbation of individual functions with Laplace noise. To this end, we establish a general framework for differentially private handling of functional data. We further design post-processing steps that ensure the perturbed functions regain the smoothness and convexity properties of the original functions while preserving the differentially private guarantees of the functional perturbation step. This methodology allows us to use any distributed coordination algorithm to solve the optimization problem on the noisy functions. Finally, we explicitly bound the magnitude of the expected distance between the perturbed and true optimizers which leads to an upper bound on the privacy-accuracy tradeoff curve. Simulations illustrate our results.

Time-invariant versus time-varying actuator scheduling in complex networks

This paper studies the benefits of time-varying actuator scheduling to the controllability of complex networks. The network dynamics are described by a single-input discrete-time linear system over an undirected graph. Taking the trace of the controllability Gramian as the measure of network controllability, we identify a new notion of nodal communicability and unveil its role in the time-varying actuator scheduling problem. We then proceed to identify conditions on the network structure that determine whether time-varying actuator scheduling is better than time-invariant actuator selection. The main conclusion of our results is that having several and heterogeneous central nodes (versus having a single highly central node) is the common factor in networks where time-varying actuator scheduling is advantageous.

Event-triggered control for nonlinear systems with time-varying input delay

This paper studies the problem of event-triggered control design for general continuous-time nonlinear systems with time-varying input delay. Our methodology is based on the concept of predictor feedback and is capable of compensating arbitrarily large known time delays. Under mild conditions, we prove that as long as the delay-free system is globally input-to-state stabilizable, it can also be globally asymptotically stabilized via piecewise-constant event-triggered control. We prove that the proposed event-triggering design does not suffer from Zeno behavior as the inter-event times are uniformly lower bounded. We further show that our design achieves exponential stability for a controllable linear system and study the trade-off between convergence speed and communication cost. Various simulations illustrate our results.