期望累积成本的最优无偏估计

Zhenyu Cui, M. Fu, Yijie Peng, Lingjiong Zhu
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引用次数: 1

摘要

我们考虑用蒙特卡罗模拟方法估计基于潜在随机过程的无限视界累积成本/回报。提出了一种基于截断随机视界上累积代价的无偏估计方法。给出了随机视界最优分布的显式形式。此外,我们通过考虑偏差和方差之间的权衡,表征了最优随机估计量优于固定截断估计量的情况。数值实验证实了理论结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimal Unbiased Estimation for Expected Cumulative Cost
We consider estimating an expected infinite-horizon cumulative 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. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. Numerical experiments substantiate the theoretical results.
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