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Commentary on “NearOptimal Algorithms for Online Matrix Prediction”
"... This piece is a commentary on the paper by Hazan et al. (2012b). In their paper, they introduce the class of (β, τ)decomposable matrices, and show that wellknown matrix regularizers and matrix classes (e.g. matrices with bounded trace norm) can be viewed as special cases of their construction. The ..."
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This piece is a commentary on the paper by Hazan et al. (2012b). In their paper, they introduce the class of (β, τ)decomposable matrices, and show that wellknown matrix regularizers and matrix classes (e.g. matrices with bounded trace norm) can be viewed as special cases of their construction
Nearoptimal algorithms for online matrix prediction
 CoRR
"... In several online prediction problems of recent interest the comparison class is composed of matrices with bounded entries. For example, in the online maxcut problem, the comparison class is matrices which represent cuts of a given graph and in online gambling the comparison class is matrices which ..."
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Cited by 13 (5 self)
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online learning algorithm, that enjoys a regret bound of Õ ( √ β τ T) for all problems in which the comparison class is composed of (β, τ)decomposable matrices. By analyzing the decomposability of cut matrices, triangular matrices, and low tracenorm matrices, we derive near optimal regret bounds
25th Annual Conference on Learning Theory NearOptimal Algorithms for Online Matrix Prediction
"... In several online prediction problems of recent interest the comparison class is composed of matrices with bounded entries. For example, in the online maxcut problem, the comparison class is matrices which represent cuts of a given graph and in online gambling the comparison class is matrices which ..."
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online learning algorithm, that enjoys a regret bound of Õ( √ β τ T) for all problems in which the comparison class is composed of (β, τ)decomposable matrices. By analyzing the decomposability of cut matrices, low tracenorm matrices and triangular matrices, we derive near optimal regret bounds
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
An Efficient Boosting Algorithm for Combining Preferences
, 1999
"... The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new boosting ..."
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Cited by 707 (18 self)
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The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a powerlaw), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information
Empirical Analysis of Predictive Algorithm for Collaborative Filtering
 Proceedings of the 14 th Conference on Uncertainty in Artificial Intelligence
, 1998
"... 1 ..."
Constrained model predictive control: Stability and optimality
 AUTOMATICA
, 2000
"... Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and t ..."
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Cited by 696 (15 self)
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from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature. In some cases the finite horizon optimal control problem solved online is exactly
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