TY - JOUR
T1 - Optimal unbiased estimation for expected cumulative discounted cost
AU - Cui, Zhenyu
AU - Fu, Michael C.
AU - Peng, Yijie
AU - Zhu, Lingjiong
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/10/16
Y1 - 2020/10/16
N2 - We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given, and explicit expressions for the optimal random truncation level are obtained, leading to a full analysis of the bias-variance tradeoff when comparing this new class of randomized estimators with traditional fixed truncation estimators. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. This comparison provides guidance on when to choose randomized estimators over fixed truncation estimators in practice. Numerical experiments substantiate the theoretical results.
AB - We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given, and explicit expressions for the optimal random truncation level are obtained, leading to a full analysis of the bias-variance tradeoff when comparing this new class of randomized estimators with traditional fixed truncation estimators. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. This comparison provides guidance on when to choose randomized estimators over fixed truncation estimators in practice. Numerical experiments substantiate the theoretical results.
KW - Computing budget allocation
KW - Cumulative costs
KW - Simulation
KW - Simulation optimization
KW - Unbiased estimation
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U2 - 10.1016/j.ejor.2020.03.072
DO - 10.1016/j.ejor.2020.03.072
M3 - Article
AN - SCOPUS:85083676084
SN - 0377-2217
VL - 286
SP - 604
EP - 618
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 2
ER -