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The Nature of Statistical Learning Theory
, 1999
"... Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based on the deve ..."
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Cited by 13236 (32 self)
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on the developed theory were proposed. This made statistical learning theory not only a tool for the theoretical analysis but also a tool for creating practical algorithms for estimating multidimensional functions. This article presents a very general overview of statistical learning theory including both
Convergence of reinforcement learning with general function approximators
 In Proceedings of the seventeenth international joint conference on artificial intelligence
, 1999
"... A key open problem in reinforcement learning is to assure convergence when using a compact hypothesis class to approximate the value function. Although the standard temporaldifference learning algorithm has been shown to converge when the hypothesis class is a linear combination of fixed basis func ..."
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Cited by 10 (0 self)
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functions, it may diverge with a general (nonlinear) hypothesis class. This paper describes the Bridge algorithm, a new method for reinforcement learning, and shows that it converges to an approximate global optimum for any agnostically learnable hypothesis class. Convergence is demonstrated on a simple
Convergence of reinforcement learning with general function approximators
"... A key open problem in reinforcement learning is to assure convergence when using a compact hypothesis class to approximate the value function. Although the standard temporaldifference learning algorithm has been shown to converge when the hypothesis class is a linear combination of fixed basis f ..."
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sis functions, it may diverge with a general (nonlinear) hypothesis class. This paper describes the Bridge algorithm, a new method for reinforcement learning, and shows that it converges to an approximate global optimum for any agnostically learnable hypothesis class. Convergence is demonstrated on a simple
Convergence of Reinforcement Learning With General Function Approximators
 In Proceedings of the seventeenth international joint conference on artificial intelligence
, 1999
"... A key open problem in reinforcement learning is to assure convergence when using a compact hypothesis class to approximate the value function. Although the standard temporaldifference learning algorithm has been shown to converge when the hypothesis class is a linear combination of fixed basis ..."
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basis functions, it may diverge with a general (nonlinear) hypothesis class. This paper describes the Bridge algorithm, a new method for reinforcement learning, and shows that it converges to an approximate global optimum for any agnostically learnable hypothesis class. Convergence is demonstrated
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 1000 (13 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
Approximation by Superpositions of a Sigmoidal Function
, 1989
"... In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate fun ..."
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Cited by 1248 (2 self)
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In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
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Cited by 916 (9 self)
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representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasiincoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function
Policy gradient methods for reinforcement learning with function approximation.
 In NIPS,
, 1999
"... Abstract Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly repres ..."
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Cited by 439 (20 self)
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policy. Large applications of reinforcement learning (RL) require the use of generalizing function approximators such neural networks, decisiontrees, or instancebased methods. The dominant approach for the last decade has been the valuefunction approach, in which all function approximation effort goes
MultiPlayer Residual Advantage Learning with General Function Approximation
 Wright Laboratory
, 1996
"... A new algorithm, advantage learning, is presented that improves on advantage updating by requiring that a single function be learned rather than two. Furthermore, advantage learning requires only a single type of update, the learning update, while advantage updating requires two different types of u ..."
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Cited by 22 (1 self)
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A new algorithm, advantage learning, is presented that improves on advantage updating by requiring that a single function be learned rather than two. Furthermore, advantage learning requires only a single type of update, the learning update, while advantage updating requires two different types
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms. We emphasize the conditions a free energy approximation must satisfy in order to be a “valid ” or “maxentnormal ” approximation. We describe the relationship between four different methods that can be used
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