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

An Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture

We formulate an Algebraic-Coding Equivalence to the Maximum Distance Separable Conjecture. Specifically, we present novel proofs of the following equivalent statements. Let $(q,k)$ be a fixed pair of integers satisfying $q$ is a prime power and $2\leq k \leq q$. We denote by $\mathcal{P}_q$ the vector space of functions from a finite field $\mathbb{F}_q$ to itself, which can be represented as the space $\mathcal{P}_q := \mathbb{F}_q[x]/(x^q-x)$ of polynomial functions. We denote by $\mathcal{O}_n \subset \mathcal{P}_q$ the set of polynomials that are either the zero polynomial, or have at most $n$ distinct roots in $\mathbb{F}_q$. Given two subspaces $Y,Z$ of $\mathcal{P}_q$, we denote by $\langle Y,Z \rangle$ their span. We prove that the following are equivalent. [A] Suppose that either: 1. $q$ is odd 2. $q$ is even and $k \not\in \{3, q-1\}$. Then there do not exist distinct subspaces $Y$ and $Z$ of $\mathcal{P}_q$ such that: 3. $dim(\langle Y, Z \rangle) = k$ 4. $dim(Y) = dim(Z) = k-1$. 5. $\langle Y, Z \rangle \subset \mathcal{O}_{k-1}$ 6. $Y, Z \subset \mathcal{O}_{k-2}$ 7. $Y\cap Z \subset \mathcal{O}_{k-3}$. [B] Suppose $q$ is odd, or, if $q$ is even, $k \not\in \{3, q-1\}$. There is no integer $s$ with $q \geq s > k$ such that the Reed-Solomon code $\mathcal{R}$ over $\mathbb{F}_q$ of dimension $s$ can have $s-k+2$ columns $\mathcal{B} = \{b_1,\ldots,b_{s-k+2}\}$ added to it, such that: 8. Any $s \times s$ submatrix of $\mathcal{R} \cup \mathcal{B}$ containing the first $s-k$ columns of $\mathcal{B}$ is independent. 9. $\mathcal{B} \cup \{[0,0,\ldots,0,1]\}$ is independent. [C] The MDS conjecture is true for the given $(q,k)$.Comment: This is version: 5.6.18. arXiv admin note: substantial text overlap with arXiv:1611.0235

Modeling spatial social complex networks for dynamical processes

The study of social networks --- where people are located, geographically, and how they might be connected to one another --- is a current hot topic of interest, because of its immediate relevance to important applications, from devising efficient immunization techniques for the arrest of epidemics, to the design of better transportation and city planning paradigms, to the understanding of how rumors and opinions spread and take shape over time. We develop a spatial social complex network (SSCN) model that captures not only essential connectivity features of real-life social networks, including a heavy-tailed degree distribution and high clustering, but also the spatial location of individuals, reproducing Zipf's law for the distribution of city populations as well as other observed hallmarks. We then simulate Milgram's Small-World experiment on our SSCN model, obtaining good qualitative agreement with the known results and shedding light on the role played by various network attributes and the strategies used by the players in the game. This demonstrates the potential of the SSCN model for the simulation and study of the many social processes mentioned above, where both connectivity and geography play a role in the dynamics.Comment: 10 pages, 6 figure

Adaptive Semi-supervised Learning for Cross-domain Sentiment Classification

We consider the cross-domain sentiment classification problem, where a sentiment classifier is to be learned from a source domain and to be generalized to a target domain. Our approach explicitly minimizes the distance between the source and the target instances in an embedded feature space. With the difference between source and target minimized, we then exploit additional information from the target domain by consolidating the idea of semi-supervised learning, for which, we jointly employ two regularizations -- entropy minimization and self-ensemble bootstrapping -- to incorporate the unlabeled target data for classifier refinement. Our experimental results demonstrate that the proposed approach can better leverage unlabeled data from the target domain and achieve substantial improvements over baseline methods in various experimental settings.Comment: Accepted to EMNLP201

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a non-trivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner- to vortex-superfluid transition, and a non-trivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a non-chiral and a chiral superfluid, both characterized by non-trivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.Comment: 5 pages, 4 figure