Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks

We study nonconvex distributed optimization in multiagent networks where the communications between nodes is modeled as a time-varying sequence of arbitrary digraphs. We introduce a novel broadcast-based distributed algorithmic framework for the (constrained) minimization of the sum of a smooth (possibly nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on Successive Convex Approximation (SCA) techniques coupled with i) a tracking mechanism instrumental to locally estimate the gradients of agents' cost functions; and ii) a novel broadcast protocol to disseminate information and distribute the computation among the agents. Asymptotic convergence to stationary solutions is established. A key feature of the proposed algorithm is that it neither requires the double-stochasticity of the consensus matrices (but only column stochasticity) nor the knowledge of the graph sequence to implement. To the best of our knowledge, the proposed framework is the first broadcast-based distributed algorithm for convex and nonconvex constrained optimization over arbitrary, time-varying digraphs. Numerical results show that our algorithm outperforms current schemes on both convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA, US

A Quantitative Approach to Investigating the Hypothesis of Prokaryotic Intron Loss

Using a novel method, we show that ordered triplets of motifs usually associated with spliceosomal intron recognition are underrepresented in the protein coding sequence of complete Thermotogae, archaeal and bacterial genomes. The underrepresentation observed does not extend to the noncoding strand, suggesting that the cause of the asymmetry is related to mRNA rather than DNA. Our data do not suggest that the underrepresentation is due to gene transfer from eukaryotes. We speculate that one possible explanation for these observations is that the protein coding sequence of Thermotogae, Archaea and Bacteria was at some time in the past subjected to selection against certain motifs appearing in an order which might initiate splicing in environments harboring a functional spliceosome. This is consistent with, but certainly does not prove, a hypothetical scenario in which at least some prokaryote lineages once possessed a functional spliceosome. Thus, we present a new quantitative method, observations obtained using the method, and a speculative discussion of a possible explanation of the observations

Distributed estimation and control of node centrality in undirected asymmetric networks

Measures of node centrality that describe the importance of a node within a network are crucial for understanding the behavior of social networks and graphs. In this paper, we address the problems of distributed estimation and control of node centrality in undirected graphs with asymmetric weight values. In particular, we focus our attention on $\alpha$-centrality, which can be seen as a generalization of eigenvector centrality. In this setting, we first consider a distributed protocol where agents compute their $\alpha$-centrality, focusing on the convergence properties of the method; then, we combine the estimation method with a consensus algorithm to achieve a consensus value weighted by the influence of each node in the network. Finally, we formulate an $\alpha$-centrality control problem which is naturally decoupled and, thus, suitable for a distributed setting and we apply this formulation to protect the most valuable nodes in a network against a targeted attack, by making every node in the network equally important in terms of {\alpha}-centrality. Simulations results are provided to corroborate the theoretical findings.Comment: published on IEEE Transactions on Automatic Control https://ieeexplore.ieee.org/abstract/document/912618

A duality-based approach for distributed min-max optimization with application to demand side management

In this paper we consider a distributed optimization scenario in which a set of processors aims at minimizing the maximum of a collection of "separable convex functions" subject to local constraints. This set-up is motivated by peak-demand minimization problems in smart grids. Here, the goal is to minimize the peak value over a finite horizon with: (i) the demand at each time instant being the sum of contributions from different devices, and (ii) the local states at different time instants being coupled through local dynamics. The min-max structure and the double coupling (through the devices and over the time horizon) makes this problem challenging in a distributed set-up (e.g., well-known distributed dual decomposition approaches cannot be applied). We propose a distributed algorithm based on the combination of duality methods and properties from min-max optimization. Specifically, we derive a series of equivalent problems by introducing ad-hoc slack variables and by going back and forth from primal and dual formulations. On the resulting problem we apply a dual subgradient method, which turns out to be a distributed algorithm. We prove the correctness of the proposed algorithm and show its effectiveness via numerical computations.Comment: arXiv admin note: substantial text overlap with arXiv:1611.0916

Chebyshev Polynomial Approximation for Distributed Signal Processing

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sensor networks. The proposed method features approximations of the graph Fourier multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be used in a distributed denoising task, and show that the communication requirements of the method scale gracefully with the size of the network.Comment: 8 pages, 5 figures, to appear in the Proceedings of the IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS), June, 2011, Barcelona, Spai