TY  - CHAP
EP  - 1908
T2  - Proceedings of the 51st IEEE International Conference on Decision and Control (IEEE CDC 2012)
N1  - 51st IEEE International Conference on Decision and Control (IEEE CDC 2012) held in Maui, Hawaii, December 10th-12th, 2012
ID  - eprints1750
UR  - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6426656&isnumber=6425800
KW  - Complexity theory
KW  -  Function approximation
KW  -  Optimal control
KW  -  Optimization
KW  -  Stochastic processes
KW  -  Vectors
Y1  - 2012///
AV  - none
TI  - Approximation Structures with Moderate Complexity in Functional Optimization and Dynamic Programming
SP  - 1902
N2  - Connections between function approximation and classes of functional optimization problems, whose admissible solutions may depend on a large number of variables, are investigated. The insights obtained in this context are exploited to analyze families of nonlinear approximation schemes containing tunable parameters and enjoying the following property: when they are used to approximate the (unknown) solutions to optimization problems, the number of parameters required to guarantee a desired accuracy grows at most polynomially with respect to the number of variables in admissible solutions. Both sigmoidal neural networks and networks with kernel units are considered as approximation structures to which the analysis applies. Finally, it is shown how the approach can be applied for the solution of finite-horizon optimal control problems via approximate dynamic programming enhancing the potentialities of recent developments in nonlinear approximation in the framework of the solution of sequential decision problems with continuous state spaces.
SN  - 978-1-4673-2065-8 
PB  - IEEE
A1  - Gaggero, Mauro
A1  - Gnecco, Giorgio
A1  - Parisini, Thomas
A1  - Sanguineti, Marcello
A1  - Zoppoli, Riccardo
ER  -