A minimalistic and easy-to-use Python module that efficiently searches for a global minimum of an expensive black-box function (e.g. optimal hyperparameters of simulation, neural network or anything that takes significant time to run). User needs to provide a function, a search domain (ranges of each input parameter) and a total number of function calls available. A code scales well on multicore CPUs and clusters: all function calls are divided into batches and each batch is evaluated in parallel.

A mathematical method behind the code is described in this arXiv note (there were few updates to the method recently): https://arxiv.org/pdf/1605.00998.pdf

Don't forget to cite this note if you are using method/code.

(a) - demo function (unknown to a method).

(b) - running a procedure using 15 evaluations.

(c) - running a procedure using 30 evaluations.

Have poetry installed (https://python-poetry.org/docs/#installation). Then run:

poetry install

Simply needs to be wrapped into a Python function.

def fun(par):
    ...
    return output

par is a vector of input parameters (a Python list), output is a scalar value to be minimized.

import blackbox as bb
def fun(x):
    return (x[0] - 1) ** 2 + (x[1] - 1) ** 2
if __name__ == '__main__':
    result = bb.minimize(f=fun, # given function
        domain=[[-5, 5], [-5, 5]], # ranges of each parameter
        budget=20, # total number of function calls available
        batch=4 # number of calls that will be evaluated in parallel
    )
    # best result (x and function value)
    print(result["best_x"])
    print(result["best_f"])
    # the entire history of evaluations
    # print(result["all_xs"])
    # print(result["all_fs"])

Important:

• All function calls are divided into batches and each batch is evaluated in parallel. Total number of batches is budget/batch. The value of batch should correspond to the number of available computational units.
• An optional parameter executor = ... should be specified within bb.minimize() in case when custom parallel engine is used (ipyparallel, dask.distributed, pathos etc). executor should be an object that has a map method.

bb.minimize() returns a dictionary with the following keys:

• "best_x" - best iteration
• "best_f" - corresponding function value
• "all_xs" - all iterations
• "all_fs" - corresponding function values

Paul Knysh (paul.knysh at gmail dot com)