Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Programs to generate Niederreiter's low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Dynamic Programming and Optimal Control
Dynamic Programming and Optimal Control
Neuro-Dynamic Programming
Approximating networks and extended Ritz method for the solution of functional optimization problems
Journal of Optimization Theory and Applications
Dynamic Programming
Deterministic design for neural network learning: an approach based on discrepancy
IEEE Transactions on Neural Networks
Lattice point sets for deterministic learning and approximate optimization problems
IEEE Transactions on Neural Networks
Computational Optimization and Applications
Design, optimization and performance evaluation of a content distribution overlay for streaming
Computer Communications
Low-discrepancy sampling for approximate dynamic programming with local approximators
Computers and Operations Research
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Dynamic Programming (DP) is known to be a standard optimization tool for solving Stochastic Optimal Control (SOC) problems, either over a finite or an infinite horizon of stages. Under very general assumptions, commonly employed numerical algorithms are based on approximations of the cost-to-go functions, by means of suitable parametric models built from a set of sampling points in the d-dimensional state space. Here the problem of sample complexity, i.e., how "fast" the number of points must grow with the input dimension in order to have an accurate estimate of the cost-to-go functions in typical DP approaches such as value iteration and policy iteration, is discussed. It is shown that a choice of the sampling based on low-discrepancy sequences, commonly used for efficient numerical integration, permits to achieve, under suitable hypotheses, an almost linear sample complexity, thus contributing to mitigate the curse of dimensionality of the approximate DP procedure.