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On constraint sampling in the linear programming approach to approximate linear programming

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2 Author(s)
de Farias, D.P. ; Dept. of Mech. Eng., Massachusetts Inst. of Technol., Cambridge, MA, USA ; Van Roy, B.

In the linear programming approach to approximate dynamic programming, one tries to solve a certain linear program - the ALP -, which has a relatively small number K of variables but an intractable number M of constraints. In this paper, we study a scheme that samples and imposes a subset of m ≪ M constraints. A natural question that arises in this context is: How must m scale with respect to K and M in order to ensure that the resulting approximation is almost as good as one given by exact solution of the ALP? We show that, under certain idealized conditions, m can be chosen independently of M and need grow only as a polynomial in K.

Published in:

Decision and Control, 2003. Proceedings. 42nd IEEE Conference on  (Volume:3 )

Date of Conference:

9-12 Dec. 2003