Synthetic Function with few Hyperparameters

An example of applying SMAC to optimize a synthetic function (2d rosenbrock function).

We use the SMAC4BB facade because it is designed for black-box function optimization. SMAC4BB uses a Gaussian Process or a set of Gaussian Processes whose hyperparameters are integrated by Markov-Chain Monte-Carlo as its surrogate model. SMAC4BB works best on numerical hyperparameter configuration space and should not be applied to the problems with large evaluation budgets (up to 1000 evaluations).

Out:

Default Value: 16916.00
Optimizing! Depending on your machine, this might take a few minutes.

import logging

logging.basicConfig(level=logging.INFO)

import numpy as np
from ConfigSpace.hyperparameters import UniformFloatHyperparameter

# Import ConfigSpace and different types of parameters
from smac.configspace import ConfigurationSpace
from smac.facade.smac_bb_facade import SMAC4BB
from smac.optimizer.acquisition import EI

# Import SMAC-utilities
from smac.scenario.scenario import Scenario

__copyright__ = "Copyright 2021, AutoML.org Freiburg-Hannover"
__license__ = "3-clause BSD"


def rosenbrock_2d(x):
    """The 2 dimensional Rosenbrock function as a toy model
    The Rosenbrock function is well know in the optimization community and
    often serves as a toy problem. It can be defined for arbitrary
    dimensions. The minimium is always at x_i = 1 with a function value of
    zero. All input parameters are continuous. The search domain for
    all x's is the interval [-5, 10].
    """

    x1 = x["x0"]
    x2 = x["x1"]

    val = 100.0 * (x2 - x1**2.0) ** 2.0 + (1 - x1) ** 2.0
    return val


if __name__ == "__main__":
    # Build Configuration Space which defines all parameters and their ranges
    cs = ConfigurationSpace()
    x0 = UniformFloatHyperparameter("x0", -5, 10, default_value=-3)
    x1 = UniformFloatHyperparameter("x1", -5, 10, default_value=-4)
    cs.add_hyperparameters([x0, x1])

    # Scenario object
    scenario = Scenario(
        {
            "run_obj": "quality",  # we optimize quality (alternatively runtime)
            "runcount-limit": 10,  # max. number of function evaluations
            "cs": cs,  # configuration space
            "deterministic": True,
        }
    )

    # Use 'gp' or 'gp_mcmc' here
    model_type = "gp"

    # Example call of the function
    # It returns: Status, Cost, Runtime, Additional Infos
    def_value = rosenbrock_2d(cs.get_default_configuration())
    print("Default Value: %.2f" % def_value)

    # Optimize, using a SMAC-object
    print("Optimizing! Depending on your machine, this might take a few minutes.")
    smac = SMAC4BB(
        scenario=scenario,
        model_type=model_type,
        rng=np.random.RandomState(42),
        acquisition_function=EI,  # or others like PI, LCB as acquisition functions
        tae_runner=rosenbrock_2d,
    )

    smac.optimize()

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Synthetic Function with few Hyperparameters