Quadratic Function

Expand to copy examples/1_basics/1_quadratic_function.py (top right)

import numpy as np
from ConfigSpace import Configuration, ConfigurationSpace, Float
from matplotlib import pyplot as plt

from smac.facade.hyperparameter_optimization_facade import HyperparameterOptimizationFacade as HPOFacade
from smac import RunHistory, Scenario

__copyright__ = "Copyright 2025, Leibniz University Hanover, Institute of AI"
__license__ = "3-clause BSD"


class QuadraticFunction:
    @property
    def configspace(self) -> ConfigurationSpace:
        cs = ConfigurationSpace(seed=0)
        x = Float("x", (-5, 5), default=-5)
        cs.add([x])

        return cs

    def train(self, config: Configuration, seed: int = 0) -> float:
        """Returns the y value of a quadratic function with a minimum we know to be at x=0."""
        x = config["x"]
        return x**2


def plot(runhistory: RunHistory, incumbent: Configuration) -> None:
    plt.figure()

    # Plot ground truth
    x = list(np.linspace(-5, 5, 100))
    y = [xi * xi for xi in x]
    plt.plot(x, y)

    # Plot all trials
    for k, v in runhistory.items():
        config = runhistory.get_config(k.config_id)
        x = config["x"]
        y = v.cost  # type: ignore
        plt.scatter(x, y, c="blue", alpha=0.1, zorder=9999, marker="o")

    # Plot incumbent
    plt.scatter(incumbent["x"], incumbent["x"] * incumbent["x"], c="red", zorder=10000, marker="x")

    plt.show()


if __name__ == "__main__":
    model = QuadraticFunction()

    # Scenario object specifying the optimization "environment"
    scenario = Scenario(model.configspace, deterministic=True, n_trials=100)

    # Now we use SMAC to find the best hyperparameters
    smac = HPOFacade(
        scenario,
        model.train,  # We pass the target function here
        overwrite=True,  # Overrides any previous results that are found that are inconsistent with the meta-data
    )

    incumbent = smac.optimize()

    # Get cost of default configuration
    default_cost = smac.validate(model.configspace.get_default_configuration())
    print(f"Default cost: {default_cost}")

    # Let's calculate the cost of the incumbent
    incumbent_cost = smac.validate(incumbent)
    print(f"Incumbent cost: {incumbent_cost}")

    # Let's plot it too
    plot(smac.runhistory, incumbent)

Description

An example of applying SMAC to optimize a quadratic function.

We use the black-box facade because it is designed for black-box function optimization. The black-box facade uses a Gaussian Process as its surrogate model. The facade works best on a numerical hyperparameter configuration space and should not be applied to problems with large evaluation budgets (up to 1000 evaluations).

CodeRun

import numpy as np
from ConfigSpace import Configuration, ConfigurationSpace, Float
from matplotlib import pyplot as plt

from smac.facade.hyperparameter_optimization_facade import HyperparameterOptimizationFacade as HPOFacade
from smac import RunHistory, Scenario

__copyright__ = "Copyright 2025, Leibniz University Hanover, Institute of AI"
__license__ = "3-clause BSD"


class QuadraticFunction:
    @property
    def configspace(self) -> ConfigurationSpace:
        cs = ConfigurationSpace(seed=0)
        x = Float("x", (-5, 5), default=-5)
        cs.add([x])

        return cs

    def train(self, config: Configuration, seed: int = 0) -> float:
        """Returns the y value of a quadratic function with a minimum we know to be at x=0."""
        x = config["x"]
        return x**2


def plot(runhistory: RunHistory, incumbent: Configuration) -> None:
    plt.figure()

    # Plot ground truth
    x = list(np.linspace(-5, 5, 100))
    y = [xi * xi for xi in x]
    plt.plot(x, y)

    # Plot all trials
    for k, v in runhistory.items():
        config = runhistory.get_config(k.config_id)
        x = config["x"]
        y = v.cost  # type: ignore
        plt.scatter(x, y, c="blue", alpha=0.1, zorder=9999, marker="o")

    # Plot incumbent
    plt.scatter(incumbent["x"], incumbent["x"] * incumbent["x"], c="red", zorder=10000, marker="x")

    plt.show()


if __name__ == "__main__":
    model = QuadraticFunction()

    # Scenario object specifying the optimization "environment"
    scenario = Scenario(model.configspace, deterministic=True, n_trials=100)

    # Now we use SMAC to find the best hyperparameters
    smac = HPOFacade(
        scenario,
        model.train,  # We pass the target function here
        overwrite=True,  # Overrides any previous results that are found that are inconsistent with the meta-data
    )

    incumbent = smac.optimize()

    # Get cost of default configuration
    default_cost = smac.validate(model.configspace.get_default_configuration())
    print(f"Default cost: {default_cost}")

    # Let's calculate the cost of the incumbent
    incumbent_cost = smac.validate(incumbent)
    print(f"Incumbent cost: {incumbent_cost}")

    # Let's plot it too
    plot(smac.runhistory, incumbent)