Cross-Entropy Elite Gaussian Update
Let elite samples reshape a search distribution and reveal how it can collapse too early.
Free theory articleLet elite samples reshape a search distribution and reveal how it can collapse too early.
Concept & interpretation
The Cross-Entropy Method (CEM) for continuous optimization iteratively refines a search distribution. In this component, we observe one iteration of updating a Gaussian search distribution to maximize an objective function. By selecting only the highest-scoring "elite" samples, the method maps the best current parameters back into a new search distribution.
Experiment with Parameters
You can interact with the Cross-Entropy Elite Gaussian Update module to see how elite selection and smoothing parameters shape the updated distribution:
- Set Target to 2 and Elite count to 2. Notice the updated distribution concentrates around the elite samples (2 and 1) with low variance.
- Change Elite count to 1. The variance collapses entirely to exactly zero, resulting in a single point mass at the elite sample. The algorithm cannot explore further!
- To prevent this premature collapse, set Smoothing to 0.5. The updated variance becomes a mixture of the old broad variance (4) and the new narrow elite variance (0), keeping the search space open for the next iteration.