Gaggero, Mauro and Gnecco, Giorgio and Parisini, Thomas and Sanguineti, Marcello and Zoppoli, Riccardo Approximation Structures with Moderate Complexity in Functional Optimization and Dynamic Programming. In: Proceedings of the 51st IEEE International Conference on Decision and Control (IEEE CDC 2012). IEEE, pp. 1902-1908. ISBN 978-1-4673-2065-8 (2012)
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Abstract
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.
| Item Type: | Book Section |
|---|---|
| Identification Number: | https://doi.org/10.1109/CDC.2012.6426656 |
| Additional Information: | 51st IEEE International Conference on Decision and Control (IEEE CDC 2012) held in Maui, Hawaii, December 10th-12th, 2012 |
| Uncontrolled Keywords: | Complexity theory, Function approximation, Optimal control, Optimization, Stochastic processes, Vectors |
| Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| Research Area: | Computer Science and Applications |
| Depositing User: | Giorgio Gnecco |
| Date Deposited: | 17 Sep 2013 07:43 |
| Last Modified: | 17 Sep 2013 07:43 |
| URI: | http://eprints.imtlucca.it/id/eprint/1750 |
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Approximation structures with moderate complexity in functional optimization and dynamic programming. (deposited 11 Sep 2013 14:40)
- Approximation Structures with Moderate Complexity in Functional Optimization and Dynamic Programming. (deposited 17 Sep 2013 07:43) [Currently Displayed]
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