ADMM-Tracking Gradient for Distributed Optimization over Asynchronous and Unreliable Networks

In this paper, we propose (i) a novel distributed algorithm for consensus optimization over networks and (ii) a robust extension tailored to deal with asynchronous agents and packet losses. The key idea is to achieve dynamic consensus on (i) the agents' average and (ii) the global descent direction by iteratively solving an online auxiliary optimization problem through a distributed implementation of the Alternating Direction Method of Multipliers (ADMM). Such a mechanism is suitably interlaced with a local proportional action steering each agent estimate to the solution of the original consensus optimization problem. First, in the case of ideal networks, by using tools from system theory, we prove the linear convergence of the scheme with strongly convex costs. Then, by exploiting the averaging theory, we extend such a first result to prove that the robust extension of our method preserves linear convergence in the case of asynchronous agents and packet losses. Further, by using the notion of Input-to-State Stability, we also guarantee the robustness of the schemes with respect to additional, generic errors affecting the agents' updates. Finally, some numerical simulations confirm our theoretical findings and show that the proposed methods outperform the existing state-of-the-art distributed methods for consensus optimization

Coping with dynamic membership, selfishness, and incomplete information: applications of probabilistic analysis and game theory

textThe emergence of large scale distributed computing networks has given increased prominence to a number of algorithmic concerns, including the need to handle dynamic membership, selfishness, and incomplete information. In this document, we outline our explorations into these algorithmic issues. We first present our results on the analysis of a graph-based coupon collecvi tor process related to load balancing for networks with dynamic membership. In addition to extending the study of the coupon collector process, our results imply load balancing properties of certain distributed hash tables. Second, we detail our results on worst case payoffs when playing buyersupplier games, against many selfish, collaborating opponents. We study optimization over the set of core vectors. We show both positive and negative results on optimizing over the cores of such games. Furthermore, we introduce and study the concept of focus point price, which answers the question: If we are constrained to play in equilibrium, how much can we lose by playing the wrong equilibrium? Finally, we present our analysis of a revenue management problem with incomplete information, the online weighted transversal matroid matching problem. In specific, we present an algorithm that delivers expected revenue within a constant of optimal in the online setting. Our results use a novel algorithm to generalize several results known for special cases of transversal matroids.Computer Science

Distributed Online Optimization with Coupled Inequality Constraints over Unbalanced Directed Networks

This paper studies a distributed online convex optimization problem, where agents in an unbalanced network cooperatively minimize the sum of their time-varying local cost functions subject to a coupled inequality constraint. To solve this problem, we propose a distributed dual subgradient tracking algorithm, called DUST, which attempts to optimize a dual objective by means of tracking the primal constraint violations and integrating dual subgradient and push sum techniques. Different from most existing works, we allow the underlying network to be unbalanced with a column stochastic mixing matrix. We show that DUST achieves sublinear dynamic regret and constraint violations, provided that the accumulated variation of the optimal sequence grows sublinearly. If the standard Slater's condition is additionally imposed, DUST acquires a smaller constraint violation bound than the alternative existing methods applicable to unbalanced networks. Simulations on a plug-in electric vehicle charging problem demonstrate the superior convergence of DUST

Scaling social media applications into geo-distributed clouds

TS51: Cloud/Grid computing and networks 3Federation of geo-distributed cloud services is a trend in cloud computing which, by spanning multiple data centers at different geographical locations, can provide a cloud platform with much larger capacities. Such a geo-distributed cloud is ideal for supporting large-scale social media streaming applications (e.g., YouTube-like sites) with dynamic contents and demands, owing to its abundant on-demand storage/bandwidth capacities and geographical proximity to different groups of users. Although promising, its realization presents challenges on how to efficiently store and migrate contents among different cloud sites (i.e. data centers), and to distribute user requests to the appropriate sites for timely responses at modest costs. These challenges escalate when we consider the persistently increasing contents and volatile user behaviors in a social media application. By exploiting social influences among users, this paper proposes efficient proactive algorithms for dynamic, optimal scaling of a social media application in a geo-distributed cloud. Our key contribution is an online content migration and request distribution algorithm with the following features: (1) future demand prediction by novelly characterizing social influences among the users in a simple but effective epidemic model; (2) oneshot optimal content migration and request distribution based on efficient optimization algorithms to address the predicted demand, and (3) a Δ(t)-step look-ahead mechanism to adjust the one-shot optimization results towards the offline optimum. We verify the effectiveness of our algorithm using solid theoretical analysis, as well as large-scale experiments under dynamic realistic settings on a home-built cloud platform. © 2012 IEEE.published_or_final_versionThe 31st Annual IEEE International Conference on Computer Communications (IEEE INFOCOM 2012), Orlando, FL., 25-30 March 2012. In IEEE Infocom Proceedings, 2012, p. 684-69

Learning and Management for Internet-of-Things: Accounting for Adaptivity and Scalability

Internet-of-Things (IoT) envisions an intelligent infrastructure of networked smart devices offering task-specific monitoring and control services. The unique features of IoT include extreme heterogeneity, massive number of devices, and unpredictable dynamics partially due to human interaction. These call for foundational innovations in network design and management. Ideally, it should allow efficient adaptation to changing environments, and low-cost implementation scalable to massive number of devices, subject to stringent latency constraints. To this end, the overarching goal of this paper is to outline a unified framework for online learning and management policies in IoT through joint advances in communication, networking, learning, and optimization. From the network architecture vantage point, the unified framework leverages a promising fog architecture that enables smart devices to have proximity access to cloud functionalities at the network edge, along the cloud-to-things continuum. From the algorithmic perspective, key innovations target online approaches adaptive to different degrees of nonstationarity in IoT dynamics, and their scalable model-free implementation under limited feedback that motivates blind or bandit approaches. The proposed framework aspires to offer a stepping stone that leads to systematic designs and analysis of task-specific learning and management schemes for IoT, along with a host of new research directions to build on.Comment: Submitted on June 15 to Proceeding of IEEE Special Issue on Adaptive and Scalable Communication Network