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Policy Improvement and the Newton-Raphson Algorithm

Published online by Cambridge University Press:  27 July 2009

P. Whittle  and
N. Komarova
P. Whittle
Affiliation:
Statistical Laboratory University of Cambridge
N. Komarova
Affiliation:
All-Union Correspondence Polytechnic Institute, Moscow, USSR
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Abstract

We show that the calculation of the infinite-horizon value function for a linear/quadratic Markov decision process by policy improvement is exactly equivalent to solution of the equilibrium Riccati equation by the Newton-Raphson method. The assertion extends to risk-sensitive and non-Markov forinulations and thus shows, for example, that the Newton-Raphson method provides an iterative algorithm for the canonical factorization of operators which shows second-order convergence and has a variational basis.

Information

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 2 , April 1988 , pp. 249 - 255
Copyright
Copyright © Cambridge University Press 1988

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References

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Whittle, P. & Kuhn, J. (1986). A Hamiltonian formulation of risk-sensitive linear/quadratic/Gaussian control. International Journal of Control 43:1–12.Google Scholar