Now, if you’re not familiar with what a “black box function” is, it basically means that we don’t know how this thing works or what goes on inside of it. It could be anything from a complex machine learning algorithm to a mysterious government program (you never know). But the good news is, Bayesian optimization can help us figure out how to make these black boxes work better without having to peek under the hood!

So Let’s begin exploring with some examples and see what this magical technique can do. First up, we have our trusty friend “Maximize a Function with Unknown Parameters” (let’s call him Max for short).

Max is a black box function that takes in two parameters (x1 and x2) and spits out some kind of output value. We don’t know exactly how he works or what goes on inside his little brain, but we do know that we want to find the best possible combination of values for those two inputs so that Max gives us the highest output score possible!

Now, here’s where Bayesian optimization comes in handy. Instead of blindly guessing at different input combinations and hoping for the best (which is what most people would do), we can use a fancy algorithm to help us find the optimal solution with much less effort.

Here’s how it works: first, we start by defining our search space this is basically just a list of all possible input combinations that Max could take (in this case, x1 and x2 can be any number between 0 and 1). Then, we randomly select a few points within that search space to test out (these are called “initial evaluations”).

Next, we use Bayesian optimization to calculate the probability of each point being the optimal solution based on our initial evaluations. This is done by creating a Gaussian process model that predicts how Max will behave for any given input combination this helps us narrow down our search space and focus on the most promising areas!

Finally, we repeat this process over and over again until we find the best possible solution (or at least until we’re satisfied with the results). And that’s it! With Bayesian optimization, you can optimize black box functions without having to know how they work or what goes on inside of them.

Resources:
– “Bayesian Optimization” by S. Mockus and M. Ginsbourger (2017) a great introduction to this topic that covers everything from basic concepts to advanced techniques.
– “A Tutorial on Bayesian Optimization for Global Optimization Problems” by J. Frazier, D. Liu, and S. Osborne (2018) another excellent resource that provides step-by-step instructions for implementing Bayesian optimization in Python using the scikit-optimize library.
– “Bayesian Optimization: A Tutorial on a Methodology to Improve Experiment Design” by J. Mockus and M. Ginsbourger (2019) this article provides an overview of Bayesian optimization and its applications in various fields, including machine learning, data science, and engineering.
– “Bayesian Optimization: A Practical Guide for Data Scientists” by S. Osborne (2020) a comprehensive guide that covers everything from basic concepts to advanced techniques, with plenty of examples and code snippets along the way!