Bayesian Optimization: probability of improvement, example

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 20:45

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.

Abstract/Summary:

This video will discuss the meaning of some acquisition functions in Bayesian Optimization by means of an example. In particular, this first video will review the basic methodology, and it will set an example up with some mean, covariance kernel and dataset to work on it. If you are familiar with these concepts (if you already watched [BOmot2EN], [BOmot3EN] and [boinopEN] ) , you may skip to [10:30] when basic review and example setup have been already explained.

Then, the meaning of the ‘probability of improvement’ heuristic (PI) for BO acquisition function is discussed. In particular, it is shown to lie on the ‘conservative side’ if good samples (below the mean) are present: if I want to improve with almost certainty, I must descend a ‘little step’ in the downward direction (sort of gradient search), and also do not drift too far away from good samples to avoid uncertainty piling up. I will improve with large probability but, possibly, I will not jump quickly to the global minimum.

Other acquisition function options take a more ‘risky’ stance: they may not improve, but when they do improve, they may improve quite a lot more than the PI sample proposal.