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81
Fast Linear Iterations for Distributed Averaging
 Systems and Control Letters
, 2003
"... We consider the problem of finding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of finding the fastest converging linear ..."
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Cited by 429 (13 self)
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We consider the problem of finding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of finding the fastest converging linear iteration can be cast as a semidefinite program, and therefore efficiently and globally solved. These optimal linear iterations are often substantially faster than several common heuristics that are based on the Laplacian of the associated graph.
Efficiency of coordinate descent methods on hugescale optimization problems
, 2010
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Posterior regularization for structured latent variable models
 Journal of Machine Learning Research
, 2010
"... We present posterior regularization, a probabilistic framework for structured, weakly supervised learning. Our framework efficiently incorporates indirect supervision via constraints on posterior distributions of probabilistic models with latent variables. Posterior regularization separates model co ..."
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Cited by 135 (8 self)
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We present posterior regularization, a probabilistic framework for structured, weakly supervised learning. Our framework efficiently incorporates indirect supervision via constraints on posterior distributions of probabilistic models with latent variables. Posterior regularization separates model complexity from the complexity of structural constraints it is desired to satisfy. By directly imposing decomposable regularization on the posterior moments of latent variables during learning, we retain the computational efficiency of the unconstrained model while ensuring desired constraints hold in expectation. We present an efficient algorithm for learning with posterior regularization and illustrate its versatility on a diverse set of structural constraints such as bijectivity, symmetry and group sparsity in several large scale experiments, including multiview learning, crosslingual dependency grammar induction, unsupervised partofspeech induction,
Joint congestion control, routing and MAC for stability and fairness in wireless networks
 IEEE Journal on Selected Areas in Communications
, 2006
"... In this work, we describe and analyze a joint scheduling, routing and congestion control mechanism for wireless networks, that asymptotically guarantees stability of the buffers and fair allocation of the network resources. The queue lengths serve as common information to different layers of the ne ..."
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Cited by 123 (23 self)
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In this work, we describe and analyze a joint scheduling, routing and congestion control mechanism for wireless networks, that asymptotically guarantees stability of the buffers and fair allocation of the network resources. The queue lengths serve as common information to different layers of the network protocol stack. Our main contribution is to prove the asymptotic optimality of a primaldual congestion controller, which is known to model different versions of TCP well.
Joint Congestion Control and Media Access Control Design for Ad Hoc Wireless Networks
 In Proc. IEEE INFOCOM
, 2005
"... Abstract—We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from content ..."
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Cited by 120 (4 self)
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Abstract—We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from contention for channel access. We present two algorithms that are not only distributed spatially, but more interestingly, they decompose vertically into two protocol layers where TCP and MAC jointly solve the system problem. The first is a primal algorithm where the MAC layer at the links generates congestion (contention) prices based on local aggregate source rates, and TCP sources adjust their rates based on the aggregate prices in their paths. The second is a dual subgradient algorithm where the MAC subalgorithm is implemented through scheduling linklayer flows according to the congestion prices of the links. Global convergence properties of these algorithms are proved. This is a preliminary step towards a systematic approach to jointly design TCP congestion control algorithms and MAC algorithms, not only to improve performance, but more importantly, to make their interaction more transparent.
Least Squares Policy Evaluation Algorithms With Linear Function Approximation
 Theory and Applications
, 2002
"... We consider policy evaluation algorithms within the context of infinitehorizon dynamic programming problems with discounted cost. We focus on discretetime dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function ..."
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Cited by 90 (13 self)
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We consider policy evaluation algorithms within the context of infinitehorizon dynamic programming problems with discounted cost. We focus on discretetime dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function approximation. The first method is a new gradientlike algorithm involving leastsquares subproblems and a diminishing stepsize, which is based on the #policy iteration method of Bertsekas and Ioffe. The second method is the LSTD(#) algorithm recently proposed by Boyan, which for # =0coincides with the linear leastsquares temporaldifference algorithm of Bradtke and Barto. At present, there is only a convergence result by Bradtke and Barto for the LSTD(0) algorithm. Here, we strengthen this result by showing the convergence of LSTD(#), with probability 1, for every # [0, 1].
On Augmented Lagrangian methods with general lowerlevel constraints
, 2005
"... Augmented Lagrangian methods with general lowerlevel constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems where the constraints are only of the lowerlevel type. Two methods of this class are introduced and analyzed. In ..."
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Cited by 80 (7 self)
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Augmented Lagrangian methods with general lowerlevel constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems where the constraints are only of the lowerlevel type. Two methods of this class are introduced and analyzed. Inexact resolution of the lowerlevel constrained subproblems is considered. Global convergence is proved using the Constant Positive Linear Dependence constraint qualification. Conditions for boundedness of the penalty parameters are discussed. The reliability of the approach is tested by means of an exhaustive comparison against Lancelot. All the problems of the Cute collection are used in this comparison. Moreover, the resolution of location problems in which many constraints of the lowerlevel set are nonlinear is addressed, employing the Spectral Projected Gradient method for solving the subproblems. Problems of this type with more than 3 × 10 6 variables and 14 × 10 6 constraints are solved in this way, using moderate computer time.
Basis function adaptation in temporal difference reinforcement learning
 Annals of Operations Research
, 2005
"... Reinforcement Learning (RL) is an approach for solving complex multistage decision problems that fall under the general framework of Markov Decision Problems (MDPs), with possibly unknown parameters. Function approximation is essential for problems with a large state space, as it facilitates compact ..."
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Cited by 75 (4 self)
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Reinforcement Learning (RL) is an approach for solving complex multistage decision problems that fall under the general framework of Markov Decision Problems (MDPs), with possibly unknown parameters. Function approximation is essential for problems with a large state space, as it facilitates compact representation and enables generalization. Linear approximation architectures (where the adjustable parameters are the weights of prefixed basis functions) have recently gained prominence due to efficient algorithms and convergence guarantees. Nonetheless, an appropriate choice of basis function is important for the success of the algorithm. In the present paper we examine methods for adapting the basis function during the learning process in the context of evaluating the value function under a fixed control policy. Using the Bellman approximation error as an optimization criterion, we optimize the weights of the basis function while simultaneously adapting the (nonlinear) basis function parameters. We present two algorithms for this problem. The first uses a gradientbased approach and the second applies the Cross Entropy method. The performance of the proposed algorithms is evaluated and compared in simulations.
An implementable proximal point algorithmic framework for nuclear norm minimization
, 2010
"... The nuclear norm minimization problem is to find a matrix with the minimum nuclear norm subject to linear and second order cone constraints. Such a problem often arises from the convex relaxation of a rank minimization problem with noisy data, and arises in many fields of engineering and science. In ..."
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Cited by 43 (7 self)
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The nuclear norm minimization problem is to find a matrix with the minimum nuclear norm subject to linear and second order cone constraints. Such a problem often arises from the convex relaxation of a rank minimization problem with noisy data, and arises in many fields of engineering and science. In this paper, we study inexact proximal point algorithms in the primal, dual and primaldual forms for solving the nuclear norm minimization with linear equality and second order cone constraints. We design efficient implementations of these algorithms and present comprehensive convergence results. In particular, we investigate the performance of our proposed algorithms in which the inner subproblems are approximately solved by the gradient projection method or the accelerated proximal gradient method. Our numerical results for solving randomly generated matrix completion problems and real matrix completion problems show that our algorithms perform favorably in comparison to several recently proposed stateoftheart algorithms. Interestingly, our proposed algorithms are connected with other algorithms that have been studied in the literature. Key words. Nuclear norm minimization, proximal point method, rank minimization, gradient projection method, accelerated proximal gradient method.
Logistic regression with an auxiliary data source
 Proceedings of the TwentySecond International Conference on Machine Learning
, 2005
"... To achieve good generalization in supervised learning, the training and testing examples are usually required to be drawn from the same source distribution. In this paper we propose a method to relax this requirement in the context of logistic regression. Assuming Dp and Da are two sets of examples ..."
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Cited by 43 (1 self)
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To achieve good generalization in supervised learning, the training and testing examples are usually required to be drawn from the same source distribution. In this paper we propose a method to relax this requirement in the context of logistic regression. Assuming Dp and Da are two sets of examples drawn from two mismatched distributions, where Da are fully labeled and Dp partially labeled, our objective is to complete the labels of Dp. We introduce an auxiliary variable μ for each example in Da to reflect its mismatch with Dp. Under an appropriate constraint the μ’s are estimated as a byproduct, along with the classifier. We also present an active learning approach for selecting the labeled examples in Dp. The proposed algorithm, called “MigratoryLogit ” or MLogit, is demonstrated successfully on simulated as well as real data sets. 1.