Finite-time bounds for fitted value iteration

Munos, Remi and Szepesvári, Csaba (2008) Finite-time bounds for fitted value iteration. Journal of Machine Learning Research, 9. pp. 815-857.

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In this paper we develop a theoretical analysis of the performance of sampling-based fitted value iteration (FVI) to solve infinite state-space, discounted-reward Markovian decision processes (MDPs) under the assumption that a generative model of the environment is available. Our main results come in the form of finite-time bounds on the performance of two versions of sampling-based FVI.The convergence rate results obtained allow us to show that both versions of FVI are well behaving in the sense that by using a sufficiently large number of samples for a large class of MDPs, arbitrary good performance can be achieved with high probability.An important feature of our proof technique is that it permits the study of weighted $L^p$-norm performance bounds. As a result, our technique applies to a large class of function-approximation methods (e.g., neural networks, adaptive regression trees, kernel machines, locally weighted learning), and our bounds scale well with the effective horizon of the MDP. The bounds show a dependence on the stochastic stability properties of the MDP: they scale with the discounted-average concentrability of the future-state distributions. They also depend on a new measure of the approximation power of the function space, the inherent Bellman residual, which reflects how well the function space is ``aligned'' with the dynamics and rewards of the MDP.The conditions of the main result, as well as the concepts introduced in the analysis, are extensively discussed and compared to previous theoretical results.Numerical experiments are used to substantiate the theoretical findings.

Item Type: ISI Article
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:31
Last Modified: 11 Dec 2012 15:31

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