What is the num_initial_points argument for Bayesian Optimization with Keras Tuner?
The Bayesian optimization algorithm selects points to test based on a balance between exploring uncertain regions and exploiting high-performing regions.  But before you've tested very many points, there's not much information to go on.  So, in this implementation you can specify a number of completely-at-random points to evaluate to start, and after that the actual Bayesian exploration begins.
Setting a high number of random points gives you guaranteed &quot;exploration&quot; points; indeed, in the documentation for the package bayesian-optimization, we find:

init_points: How many steps of random exploration you want to perform. Random exploration can help by diversifying the exploration space.

(The default is 5 in that package, and 3 times the dimension in keras-tuner.)
That said, you can also make the algorithm focus more or less on exploration/exploitation directly, using the beta parameter (kappa in bayesian-optimization, see this example notebook).