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We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses Hessian information to accelerate convergence. We analyze our method under the general asynchronous model of computation, in which each function is selected infinitely often with possibly unbounded (but sublinear) delay. For strongly convex problems, we establish linear convergence for the SUCAG method. When the initialization point is sufficiently close to the optimal solution, the established convergence rate is only dependent on the condition number of the problem, making it strictly faster than the known rate for the SAGA method. Furthermore, we describe a Markov-driven approach of implementing the SUCAG method in a distributed asynchronous multi-agent setting, via gossiping along a random walk on an undirected communication graph. We show that our analysis applies as long as the graph is connected and, notably, establishes an asymptotic linear convergence rate that is robust to the graph topology. Numerical results demonstrate the merits of our algorithm over existing methods. 

We establish average consensus on graphs with dynamic topologies prescribed by evolutionary games among strategic agents. Each agent possesses a private reward function and dynamically decides whether to create new links and/or whether to delete existing ones in a selfish and decentralized fashion, as indicated by a certain randomized mechanism. This model incurs a time-varying and state-dependent graph topology for which traditional consensus analysis is not applicable. We prove asymptotic average consensus almost surely and in mean square for any initial condition and graph topology. In addition, we establish exponential convergence in expectation. Our results are validated via simulation studies on random networks. 

This paper proposes a data-driven method to pinpoint the source of a new emerging dynamical phenomenon in the power grid, referred to “forced oscillations” in the difficult but highly risky case where there is a resonance phenomenon. By exploiting the low-rank and sparse properties of synchrophasor measurements, the localization problem is formulated as a matrix decomposition problem, which can be efficiently solved by the exact augmented Lagrange multiplier algorithm. An online detection scheme is developed based on the problem formulation. The data-driven nature of the proposed method allows for a very efficient implementation. The efficacy of the proposed method is illustrated in a 68-bus power system. The proposed method may possibly be more broadly useful in other situations for identifying the source of forced oscillations in resonant systems. Index Terms—Forced oscillations, resonant systems, phasor measurement unit (PMU), robust principal component analysis (RPCA), Big Data.