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Fitted Value Function Iteration with Probability One Contractions

This page collects files and computer code for the paper Fitted Value Function Iteration with Probability One Contractions by Jeno Pal and John Stachurski.

Publication Details

Fitted Value Function Iteration with Probability One Contractions
Jeno Pal and John Stachurski
Journal of Economic Dynamics and Control, 37 (2013) 251–264.


This paper studies a value function iteration algorithm based on nonexpansive function approximation and Monte Carlo integration that can be applied to almost all stationary dynamic programming problems. The method can be represented using a randomized fitted Bellman operator and a corresponding algorithm that is shown to be globally convergent with probability one. When additional restrictions are imposed, an O_P(n^{-1/2}) rate of convergence for Monte Carlo error is obtained.


Python code can be found in the repository, and also on the Google code site. Matlab code is posted as well. The latter is written by my RA Alex Olssen, and replicates figure 3 in the paper. There are two files, and the content is well documented and self-explanitory.

Some general comments on coding are as follows: First, the paper suggests kernel smoothers as one possible nonexpansive approximation method, and linear interpolation as another. In subsequent experiments, we've found that kernel smoothers are usually a waste of time. Linear interpolation is almost always easier and better. A second comment is that if you are working in a low dimensional setting and find that Gaussian quadrature is more efficient than Monte Carlo, there's no problems with using it: Gaussian quadrature paired with a nonexpansive approximator should again be nonexpansive.


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