Title :
Optimality of LSTD and its Relation to MC
Author :
Grunewalder, S. ; Hochreiter, Sepp ; Obermayer, Klaus
Author_Institution :
Univ. of Technol. Berlin, Berlin
Abstract :
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.
Keywords :
Markov processes; Monte Carlo methods; convex programming; estimation theory; least squares approximations; statistical analysis; Monte Carlo method; acyclic Markov reward process; convex loss function; least-squares temporal difference estimator; statistical estimation theory; Concrete; Convergence; Learning; Materials requirements planning; Monte Carlo methods; Neural networks; Risk analysis; State estimation; Upper bound; Yield estimation;
Conference_Titel :
Neural Networks, 2007. IJCNN 2007. International Joint Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-4244-1379-9
Electronic_ISBN :
1098-7576
DOI :
10.1109/IJCNN.2007.4370979
