How is the iteration threshold $\gamma_i$ defined and when does the cross-entropy loop stop?

Q: How is the iteration threshold $\gamma_i$ defined and when does the cross-entropy loop stop?

The iteration threshold $\gamma_i$ is defined as the empirical $(1-p)$-quantile of the current batch of samples drawn from the proposal distribution. The loop stops when this threshold $\gamma_i$ is greater than or equal to the target rare-event threshold $\gamma$.

The iteration threshold

\gamma_i

is defined as the empirical

(1-p)

-quantile of the current batch of samples drawn from the proposal distribution. The loop stops when this threshold

\gamma_i

is greater than or equal to the target rare-event threshold

\gamma

Conditions

Samples are drawn from the current proposal distribution.
The elite fraction parameter $p$ is set to 0.05.
The target threshold is $\gamma=5$ .

Reasoning, step by step

Draw a batch of samples from the current proposal.
Compute the empirical 95% quantile of these samples to get $\gamma_i$ .
Compare $\gamma_i$ to the target threshold $\gamma$ .
If $\gamma_i \ge \gamma$ , stop the iteration.

Example

The code shows `gamma_i = np.quantile(Xs, 1-p)` and `if gamma_i >= gamma: break` with ` $p = 0.05$ `. The speaker says the threshold for this iteration is set to be the 95% threshold of the X samples, and if this is above the overall goal of gamma, they stop iterating.

Common misconceptions

Assuming $\gamma_i$ is a fixed constant throughout the iterations.
Thinking the loop stops when the sample mean exceeds $\gamma$ .

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How is the iteration threshold γi\gamma_iγi​ defined and when does the cross-entropy loop stop?