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Optimization with EM and ExpectationConjugateGradient
, 2003
"... We show a close relationship between the Expectation  Maximization (EM) algorithm and direct optimization algorithms such as gradientbased methods for parameter learning. ..."
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We show a close relationship between the Expectation  Maximization (EM) algorithm and direct optimization algorithms such as gradientbased methods for parameter learning.
Lagrange Dual Decomposition for Finite Horizon Markov Decision Processes
"... Abstract. Solving finitehorizon Markov Decision Processes with stationary policies is a computationally difficult problem. Our dynamic dual decomposition approach uses Lagrange duality to decouple this hard problem into a sequence of tractable subproblems. The resulting procedure is a straightforw ..."
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Abstract. Solving finitehorizon Markov Decision Processes with stationary policies is a computationally difficult problem. Our dynamic dual decomposition approach uses Lagrange duality to decouple this hard problem into a sequence of tractable subproblems. The resulting procedure is a straightforward modification of standard nonstationary Markov Decision Process solvers and gives an upperbound on the total expected reward. The empirical performance of the method suggests that not only is it a rapidly convergent algorithm, but that it also performs favourably compared to standard planning algorithms such as policy gradients and lowerbound procedures such as Expectation Maximisation.
Sequence labeling · Stochastic gradient descent
"... Periodic stepsize adaptation in secondorder gradient ..."
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Abstract Efficient Optimization Algorithms for Learning
, 2003
"... Many problems in machine learning and pattern recognition ultimately reduce to the optimization of a scalar valued function. A variety of general techniques exist for optimizing such objective functions. We study the general class of bound optimization algorithms – including ExpectationMaximizati ..."
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Many problems in machine learning and pattern recognition ultimately reduce to the optimization of a scalar valued function. A variety of general techniques exist for optimizing such objective functions. We study the general class of bound optimization algorithms – including ExpectationMaximization, Iterative Scaling, Nonnegative Matrix Factorization, ConcaveConvex Procedure – and their relationship to direct optimization algorithms such as gradientbased methods for parameter learning. We also provide a theoretical analysis of the convergence properties of bound optimization algorithms and identify analytic conditions under which these optimizers exhibit quasiNewton behavior, and conditions under which they possess poor, firstorder convergence. Motivated by these analyses, we interpret and analyze their convergence properties and provide some recipes for preprocessing input to these algorithms to yield faster convergence behavior. Our presented analysis also allows us to design several algorithms for practical optimization, that possess superior convergence over standard existing methods. ii Dedication