Cross-entropy Method - Estimation Via Importance Sampling

Estimation Via Importance Sampling

Consider the general problem of estimating the quantity, where is some performance function and is a member of some parametric family of distributions. Using importance sampling this quantity can be estimated as, where is a random sample from . For positive, the theoretically optimal importance sampling density (pdf)is given by . This, however, depends on the unknown . The CE method aims to approximate the optimal pdf by adaptively selecting members of the parametric family that are closest (in the Kullback-Leibler sense) to the optimal pdf .

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