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Fitted Value Function Iteration With Probability One Contractions
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Abstract
This paper studies a value function iteration algorithm that can be applied to almost all stationary dynamic programming problems. Using nonexpansive function approximation and Monte Carlo integration, we develop a randomized fitted Bellman operator and a corresponding algorithm that is globally convergent with probability one. When additional restrictions are imposed, an OP(n-1/2) rate of convergence for Monte Carlo error is obtained.