二次函数

展开以复制 examples/1_basics/1_quadratic_function.py （右上角）

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)

描述

一个将 SMAC 应用于优化二次函数的示例。

我们使用黑盒外观，因为它专为黑盒函数优化而设计。黑盒外观使用 高斯过程 作为其代理模型。该外观最适合数值超参数配置空间，不应应用于具有大量评估预算（最多 1000 次评估）的问题。

代码运行

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)