Universal approximation using radial-basis-function networks
Neural Computation
Scenarios and policy aggregation in optimization under uncertainty
Mathematics of Operations Research
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Approximation and Estimation Bounds for Artificial Neural Networks
Machine Learning - Special issue on computational learning theory
Regularization theory and neural networks architectures
Neural Computation
The nature of statistical learning theory
The nature of statistical learning theory
Neuro-Dynamic Programming
Approximating networks and extended Ritz method for the solution of functional optimization problems
Journal of Optimization Theory and Applications
Error Estimates for Approximate Optimization by the Extended Ritz Method
SIAM Journal on Optimization
A recursive algorithm for nonlinear least-squares problems
Computational Optimization and Applications
Efficient sampling in approximate dynamic programming algorithms
Computational Optimization and Applications
Step decision rules for multistage stochastic programming: A heuristic approach
Automatica (Journal of IFAC)
Accuracy of suboptimal solutions to kernel principal component analysis
Computational Optimization and Applications
Learning with generalization capability by kernel methods of bounded complexity
Journal of Complexity
Comparison of worst case errors in linear and neural network approximation
IEEE Transactions on Information Theory
Convergent on-line algorithms for supervised learning in neural networks
IEEE Transactions on Neural Networks
Distributed-information neural control: the case of dynamic routing in traffic networks
IEEE Transactions on Neural Networks
Optimization-based learning with bounded error for feedforward neural networks
IEEE Transactions on Neural Networks
Deterministic design for neural network learning: an approach based on discrepancy
IEEE Transactions on Neural Networks
Adaptive value function approximation for continuous-state stochastic dynamic programming
Computers and Operations Research
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Two methods of approximate solution are developed for T-stage stochastic optimal control (SOC) problems, aimed at obtaining finite-horizon management policies for water resource systems. The presence of uncertainties, such as river and rain inflows, is considered. Both approaches are based on the use of families of nonlinear functions, called "one-hidden-layer networks" (OHL networks), made up of linear combinations of simple basis functions containing parameters to be optimized. The first method exploits OHL networks to obtain an accurate approximation of the cost-to-go functions in the dynamic programming procedure for SOC problems. The approximation capabilities of OHL networks are combined with the properties of deterministic sampling techniques aimed at obtaining uniform samplings of high-dimensional domains. In the second method, admissible solutions to SOC problems are constrained to take on the form of OHL networks, whose parameters are determined in such a way to minimize the cost functional associated with SOC problems. Exploiting these tools, the two methods are able to cope with the so-called "curse of dimensionality," which strongly limits the applicability of existing techniques to high-dimensional water resources management in the presence of uncertainties. The theoretical bases of the two approaches are investigated. Simulation results show that the proposed methods are effective for water resource systems of high dimension.