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A Class of Decision Processes Showing Policy-Improvement/Newton–Raphson Equivalence

Published online by Cambridge University Press:  27 July 2009

P. Whittle
P. Whittle
Affiliation:
Statistical LaboratoryUniversity of Cambridge, Cambridge CB2 1SB, United Kingdom
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Abstract

A condition expressed in Eq. (7) is given which, with one simplifying regularity condition, ensures that the policy-improvement algorithm is equivalent to application of the Newton–Raphson algorithm to an optimality condition. It is shown that this condition covers the two known cases of such equivalence, and another example is noted. The condition is believed to be necessary to within transformations of the problem, but this has not been proved.

Information

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 397 - 403
Copyright
Copyright © Cambridge University Press 1989

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References

McNamara, J.M. (1989). Policy improvement and the Newton–Raphson algorithm for renewal reward processes. Probability in the Engineering and Informational Sciences 3: 393–396.CrossRefGoogle Scholar
Whittle, P. (1981). Risk-sensitive linear/quadratic/Gaussian control. Advances in Applied Probability 13: 764–777.CrossRefGoogle Scholar
Whittle, P. & Komarova, N. (1988). Policy improvement and the Newton–Raphson algorithm. Probability in the Engineering and Informational Sciences 2: 249–255.CrossRefGoogle Scholar