Real-time data-driven optimization and control problems over networks, such as in traffic or energy systems, may require sensitive information of participating agents to calculate solutions and decision variables. Adversaries with access to coordination signals may potentially decode information on individual agents and put privacy at risk. We use the Inexact Alternating Minimization Algorithm to instantiate local differential privacy for distributed optimization, addressing situations in which individual agents need to protect their individual data, in the form of optimization parameters, from all other agents and any central authority. This mechanism allows agents to customize their own privacy level based on local needs and parameter sensitivities. The resulting algorithm works across a large family of convex distributed optimization problems. We implement the method on a distributed optimal power flow problem that aims to prevent overload on critical branches in a radial network. ... Read more

This paper focuses on the design of an asynchronous dual solver suitable for model predictive control (MPC) applications. The proposed solver relies on a state-of-the-art variance reduction (VR) scheme, previously used in the context of stochastic proximal gradient methods (Prox-SVRG), and on the alternating minimization algorithm (AMA). The resultant algorithm, a stochastic AMA with VR (SVR-AMA), shows geometric convergence (in the expectation) to a suboptimal solution of the MPC problem and, compared to other state-of-the-art dual asynchronous algorithms, allows one to tune the probability of the asynchronous updates to improve the quality of the estimates. Two novel accelerated versions of the Prox-SVRG (and, by duality, of SVR-AMA) are also provided. We apply the proposed algorithm to a specific class of splitting methods, that is, the decomposition along the length of the prediction horizon. Numerical results on the longitudinal control problem of an Airbus passenger aircraft show the benefits that we can gain in terms of computation time when using our proposed solver with an adaptive probability distribution. ... Read more