Asynchronous Distributed ADMM for Large-Scale Optimization- Part I: Algorithm and Convergence Analysis

Aiming at solving large-scale learning problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the learning problem as a consensus problem, the ADMM can be used to solve the consensus problem in a fully parallel fashion over a computer network with a star topology. However, traditional synchronized computation does not scale well with the problem size, as the speed of the algorithm is limited by the slowest workers. This is particularly true in a heterogeneous network where the computing nodes experience different computation and communication delays. In this paper, we propose an asynchronous distributed ADMM (AD-AMM) which can effectively improve the time efficiency of distributed optimization. Our main interest lies in analyzing the convergence conditions of the AD-ADMM, under the popular partially asynchronous model, which is defined based on a maximum tolerable delay of the network. Specifically, by considering general and possibly non-convex cost functions, we show that the AD-ADMM is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points as long as the algorithm parameters are chosen appropriately according to the network delay. We further illustrate that the asynchrony of the ADMM has to be handled with care, as slightly modifying the implementation of the AD-ADMM can jeopardize the algorithm convergence, even under a standard convex setting.Comment: 37 page

Content Caching and Delivery over Heterogeneous Wireless Networks

Emerging heterogeneous wireless architectures consist of a dense deployment of local-coverage wireless access points (APs) with high data rates, along with sparsely-distributed, large-coverage macro-cell base stations (BS). We design a coded caching-and-delivery scheme for such architectures that equips APs with storage, enabling content pre-fetching prior to knowing user demands. Users requesting content are served by connecting to local APs with cached content, as well as by listening to a BS broadcast transmission. For any given content popularity profile, the goal is to design the caching-and-delivery scheme so as to optimally trade off the transmission cost at the BS against the storage cost at the APs and the user cost of connecting to multiple APs. We design a coded caching scheme for non-uniform content popularity that dynamically allocates user access to APs based on requested content. We demonstrate the approximate optimality of our scheme with respect to information-theoretic bounds. We numerically evaluate it on a YouTube dataset and quantify the trade-off between transmission rate, storage, and access cost. Our numerical results also suggest the intriguing possibility that, to gain most of the benefits of coded caching, it suffices to divide the content into a small number of popularity classes.Comment: A shorter version is to appear in IEEE INFOCOM 201

Supplier Choice: Market Selection under Uncertainty.

Suppliers and Manufacturers generally have some say in which subset of all possible demand they will meet. In some cases that choice is implicit through pricing decisions and feature selection. Other times it is made explicitly by choosing only specific regions to stock a product in. This thesis includes models using both approaches and incorporates random demands. We present several methods for choosing a subset of all candidate customers given uncertain demands. In this thesis we consider four models of demand selection. The first two research problems consider market selection, which has been studied in the literature. The Selective Newsvendor Problem (SNP) looks at a decision maker choosing a subset of candidate markets to serve, and then receiving revenues and paying newsvendor-type costs based on the selected collection. In this thesis we consider a generalization with normally distributed demands which includes a multi-period problem as a special case and develop both exact and heuristic algorithms to solve it. When demands are not normally distributed, the problem is considerably more complex and is in general NP-hard. We develop an approximation algorithm using sample average approximation and a rounding approach to efficiently solve the problem. In addition to the work on market selection, we propose two other models for demand selection. We study auctions as a tool for a supplier with a fixed capacity to allocate the limited supply to retailers with newsvendor-type costs. Finally, we present a model for a supplier who must ensure demand is met in all markets, but has the option to work with subsidiary suppliers to meet that demand.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120864/1/zstrinka_1.pd

Design of limited feedback for robust MMSE precoding in multiuser MISO systems

[Resumen] En este trabajo consideramos un sistema multiusuario con múltiples antenas en transmisión y una única antena en cada uno de los usuarios receptores y que se denota por brevedad como MU-MISO, del inglés Multi–User Multiple–Input/Single–Output. Este modelo MU–MISO se ajusta perfectamente al enlace descendente de un sistema de comunicaciones móviles, donde múltiples antenas situadas en la estación base envían información a varios usuarios dentro de su zona de cobertura y cuyos terminales móviles disponen generalmente de una única antena. Este canal descendente se denomina también canal de difusión (BC, del inglés Broadcast Channel). Cuando se considera un canal de difusión, el transmisor centralizado tiene claramente más grados de libertad que cada uno de los receptores descentralizados, por lo que es más apropiado separar las señales aplicando precodificación en transmisión. Para poder realizar el diseño de los parámetros del precodificador, el transmisor necesita conocer la información de canal (CSI, en inglés Channel State Information) correspondiente a los distintos usuarios receptores. En el caso de sistemas FDD (del inglés, Frequency Division Duplex), esta información puede obtenerse (al menos parcialmente) mediante realimentación, siempre tras haber aplicado un proceso de cuantificación de la información enviada con el objetivo de adaptarse a las condiciones de ancho de banda limitado del canal de retorno

Optimization techniques and new methods for boradcast encryption and traitor tracing schemes

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2012.Thesis (Ph. D.) -- Bilkent University, 2012.Includes bibliographical refences.In the last few decades, the use of digital content increased dramatically. Many forms of digital products in the form of CDs, DVDs, TV broadcasts, data over the Internet, entered our life. Classical cryptography, where encryption is done for only one recipient, was not able to handle this change, since its direct use leads to intolerably expensive transmissions. Moreover, new concerns regarding the commercial aspect arised. Since digital commercial contents are sold to various customers, unauthorized copying by malicious actors became a major concern and it needed to be prevented carefully. Therefore, a new research area called digital rights management (DRM) has emerged. Within the scope of DRM, new cryptographic primitives are proposed. In this thesis, we consider three of these: broadcast encryption (BE), traitor tracing (TT), and trace and revoke (T&R) schemes and propose methods to improve the performances and capabilities of these primitives. Particularly, we first consider profiling the recipient set in order to improve transmission size in the most popular BE schemes. We then investigate and solve the optimal free rider assignment problem for one of the most efficient BE schemes so far. Next, we attempt to close the non-trivial gap between BE and T&R schemes by proposing a generic method for adding traitor tracing capability to BE schemes and thus obtaining a T&R scheme. Finally, we investigate an overlooked problem: privacy of the recipient set in T&R schemes. Right now, most schemes do not keep the recipient set anonymous, and everybody can see who received a particular content. As a generic solution to this problem, we propose a method for obtaining anonymous T&R scheme by using anonymous BE schemes as a primitive.Ak, MuratPh.D

Flexible Demand in Smart Grids - Modeling and Coordination

The economic analysis of smart grid capabilities needs to incorporate physical boundaries as hard constraints which need to be facilitated by means of flexibility potentials and intelligent dispatching. Due to the distributed nature of demand, economic coordination also needs to be able to facilitate a multitude of individual agents. Questions concerning the modeling and coordination of an active demand side are addressed using tools and techniques from information systems and economics

Local Dynamic Reactive Power for Correction of System Voltage Problems

Distribution systems are experiencing outages due to a phenomenon known as local voltage collapse. Local voltage collapse is occurring in part because modern air conditioner compressor motors are much more susceptible to stalling during a voltage dip than older motors. These motors can stall in less than 3 cycles (.05s) when a fault, such as on the sub-transmission system, causes voltage to sag to 70 to 60%. The reasons for this susceptibility are discussed in the report. During the local voltage collapse, voltages are depressed for a period of perhaps one or two minutes. There is a concern that these local events are interacting together over larger areas and may present a challenge to system reliability. An effective method of preventing local voltage collapse is the use of voltage regulation from Distributed Energy Resources (DER) that can supply or absorb reactive power. DER, when properly controlled, can provide a rapid correction to voltage dips and prevent motor stall. This report discusses the phenomenon and causes of local voltage collapse as well as the control methodology we have developed to counter voltage sag. The problem is growing because of the use of low inertia, high efficiency air conditioner (A/C) compressor motors and because the use of electric A/C is growing in use and becoming a larger percentage of system load. A method for local dynamic voltage regulation is discussed which uses reactive power injection or absorption from local DER. This method is independent, rapid, and will not interfere with conventional utility system voltage control. The results of simulations of this method are provided. The method has also been tested at the ORNL s Distributed Energy Communications and Control (DECC) Laboratory using our research inverter and synchronous condenser. These systems at the DECC Lab are interconnected to an actual distribution system, the ORNL distribution system, which is fed from TVA s 161kV sub-transmission backbone. The test results are also provided and discussed. The simulations and testing show that local voltage control from DER can prevent local voltage collapse. The results also show that the control can be provided so quickly, within 0.5 seconds, that is does not interfere with conventional utility methods