Distributed Large Scale Network Utility Maximization

Recent work by Zymnis et al. proposes an efficient primal-dual interior-point method, using a truncated Newton method, for solving the network utility maximization (NUM) problem. This method has shown superior performance relative to the traditional dual-decomposition approach. Other recent work by Bickson et al. shows how to compute efficiently and distributively the Newton step, which is the main computational bottleneck of the Newton method, utilizing the Gaussian belief propagation algorithm. In the current work, we combine both approaches to create an efficient distributed algorithm for solving the NUM problem. Unlike the work of Zymnis, which uses a centralized approach, our new algorithm is easily distributed. Using an empirical evaluation we show that our new method outperforms previous approaches, including the truncated Newton method and dual-decomposition methods. As an additional contribution, this is the first work that evaluates the performance of the Gaussian belief propagation algorithm vs. the preconditioned conjugate gradient method, for a large scale problem.Comment: In the International Symposium on Information Theory (ISIT) 200

Distributive Network Utility Maximization (NUM) over Time-Varying Fading Channels

Distributed network utility maximization (NUM) has received an increasing intensity of interest over the past few years. Distributed solutions (e.g., the primal-dual gradient method) have been intensively investigated under fading channels. As such distributed solutions involve iterative updating and explicit message passing, it is unrealistic to assume that the wireless channel remains unchanged during the iterations. Unfortunately, the behavior of those distributed solutions under time-varying channels is in general unknown. In this paper, we shall investigate the convergence behavior and tracking errors of the iterative primal-dual scaled gradient algorithm (PDSGA) with dynamic scaling matrices (DSC) for solving distributive NUM problems under time-varying fading channels. We shall also study a specific application example, namely the multi-commodity flow control and multi-carrier power allocation problem in multi-hop ad hoc networks. Our analysis shows that the PDSGA converges to a limit region rather than a single point under the finite state Markov chain (FSMC) fading channels. We also show that the order of growth of the tracking errors is given by O(T/N), where T and N are the update interval and the average sojourn time of the FSMC, respectively. Based on this analysis, we derive a low complexity distributive adaptation algorithm for determining the adaptive scaling matrices, which can be implemented distributively at each transmitter. The numerical results show the superior performance of the proposed dynamic scaling matrix algorithm over several baseline schemes, such as the regular primal-dual gradient algorithm

NUMFabric: Fast and Flexible Bandwidth Allocation in Datacenters

We present xFabric, a novel datacenter transport design that provides flexible and fast bandwidth allocation control. xFabric is flexible: it enables operators to specify how bandwidth is allocated amongst contending flows to optimize for different service-level objectives such as minimizing flow completion times, weighted allocations, different notions of fairness, etc. xFabric is also very fast, it converges to the specified allocation one-to-two order of magnitudes faster than prior schemes. Underlying xFabric, is a novel distributed algorithm that uses in-network packet scheduling to rapidly solve general network utility maximization problems for bandwidth allocation. We evaluate xFabric using realistic datacenter topologies and highly dynamic workloads and show that it is able to provide flexibility and fast convergence in such stressful environments.Google Faculty Research Awar

Distributed optimization of multi-agent systems: Framework, local optimizer, and applications

Convex optimization problem can be solved in a centralized or distributed manner. Compared with centralized methods based on single-agent system, distributed algorithms rely on multi-agent systems with information exchanging among connected neighbors, which leads to great improvement on the system fault tolerance. Thus, a task within multi-agent system can be completed with presence of partial agent failures. By problem decomposition, a large-scale problem can be divided into a set of small-scale sub-problems that can be solved in sequence/parallel. Hence, the computational complexity is greatly reduced by distributed algorithm in multi-agent system. Moreover, distributed algorithm allows data collected and stored in a distributed fashion, which successfully overcomes the drawbacks of using multicast due to the bandwidth limitation. Distributed algorithm has been applied in solving a variety of real-world problems. Our research focuses on the framework and local optimizer design in practical engineering applications. In the first one, we propose a multi-sensor and multi-agent scheme for spatial motion estimation of a rigid body. Estimation performance is improved in terms of accuracy and convergence speed. Second, we develop a cyber-physical system and implement distributed computation devices to optimize the in-building evacuation path when hazard occurs. The proposed Bellman-Ford Dual-Subgradient path planning method relieves the congestion in corridor and the exit areas. At last, highway traffic flow is managed by adjusting speed limits to minimize the fuel consumption and travel time in the third project. Optimal control strategy is designed through both centralized and distributed algorithm based on convex problem formulation. Moreover, a hybrid control scheme is presented for highway network travel time minimization. Compared with no controlled case or conventional highway traffic control strategy, the proposed hybrid control strategy greatly reduces total travel time on test highway network

Distributed Newton-type algorithms for network resource allocation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 99-101).Most of today's communication networks are large-scale and comprise of agents with local information and heterogeneous preferences, making centralized control and coordination impractical. This motivated much interest in developing and studying distributed algorithms for network resource allocation problems, such as Internet routing, data collection and processing in sensor networks, and cross-layer communication network design. Existing works on network resource allocation problems rely on using dual decomposition and first-order (gradient or subgradient) methods, which involve simple computations and can be implemented in a distributed manner, yet suffer from slow rate of convergence. Second-order methods are faster, but their direct implementation requires computation intensive matrix inversion operations, which couple information across the network, hence cannot be implemented in a decentralized way. This thesis develops and analyzes Newton-type (second-order) distributed methods for network resource allocation problems. In particular, we focus on two general formulations: Network Utility Maximization (NUM), and network flow cost minimization problems. For NUM problems, we develop a distributed Newton-type fast converging algorithm using the properties of self-concordant utility functions. Our algorithm utilizes novel matrix splitting techniques, which enable both primal and dual Newton steps to be computed using iterative schemes in a decentralized manner with limited information exchange. Moreover, the step-size used in our method can be obtained via an iterative consensus-based averaging scheme. We show that even when the Newton direction and the step-size in our method are computed within some error (due to finite truncation of the iterative schemes), the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood. Simulation results demonstrate significant convergence rate improvement of our algorithm relative to the existing subgradient methods based on dual decomposition. The second part of the thesis presents a distributed approach based on a Newtontype method for solving network flow cost minimization problems. The key component of our method is to represent the dual Newton direction as the limit of an iterative procedure involving the graph Laplacian, which can be implemented based only on local information. Using standard Lipschitz conditions, we provide analysis for the convergence properties of our algorithm and show that the method converges superlinearly to an explicitly characterized error neighborhood, even when the iterative schemes used for computing the Newton direction and the stepsize are truncated. We also present some simulation results to illustrate the significant performance gains of this method over the subgradient methods currently used.by Ermin Wei.S.M