Note: On the Interchange of Derivative and Expectation for Likelihood Ratio Derivative Estimators
探讨似然比梯度估计中导数与期望交换的充分条件，提出更易验证的变体，并给出导数估计量具有有限矩的条件，举例说明满足交换条件但方差无限的估计量。
Sufficient conditions for the validity of interchange between derivative and expectation, in the context of likelihood ratio gradient estimation, were given in L'Ecuyer (1990). The aim of this paper is to shed additional light on these conditions and introduce specific variants of them, which are often easier to check. Sufficient conditions for the derivative estimator to have finite moments up to a given order are also given and illustrated by examples. In particular, we give an example of an unbiased derivative estimator which satisfies the interchange conditions but which has infinite variance.