Optimality of LSTD and its relation to MC

Grunewalder, Steffen and Hochreiter, Sepp and Obermayer, Klaus (2007) Optimality of LSTD and its relation to MC. In: International Joint Conference on Neural Networks, 2007. IJCNN 2007. IEEE. ISBN 9781424413799

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In this analytical study we compare the risk of the Monte Carlo (MC) and the least-squares TD (LSTD) estimator. We prove that for the case of acyclic Markov Reward Processes (MRPs) LSTD has minimal risk for any convex loss function in the class of unbiased estimators. When comparing the Monte Carlo estimator, which does not assume a Markov structure, and LSTD, we find that the Monte Carlo estimator is equivalent to LSTD if both estimators have the same amount of information. Theoretical results are supported by an empirical evaluation of the estimators.

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07 Mar 2017 11:28
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18 Sep 2023 02:34