Example for constraints in a hybrid searchspace

Example for optimizing a synthetic test functions in a hybrid space with one constraint in the discrete subspace and one constraint in the continuous subspace. All test functions that are available in BoTorch are also available here and wrapped via the botorch_function_wrapper. This example assumes some basic familiarity with using BayBE. We thus refer to campaign for a basic example. Also, there is a large overlap with other examples with regards to using the test function. We thus refer to discrete_space for details on this aspect.

Necessary imports for this example

import numpy as np
from botorch.test_functions import Rastrigin

from baybe import Campaign
from baybe.constraints import (
    ContinuousLinearEqualityConstraint,
    DiscreteSumConstraint,
    ThresholdCondition,
)
from baybe.objectives import SingleTargetObjective
from baybe.parameters import NumericalContinuousParameter, NumericalDiscreteParameter
from baybe.searchspace import SearchSpace
from baybe.targets import NumericalTarget
from baybe.utils.botorch_wrapper import botorch_function_wrapper

Defining the test function

See discrete_space for details.

DIMENSION = 4
TestFunctionClass = Rastrigin

Specify a numerical stride for discrete parameters. If you make it too small, it will make calculations expensive. If you make it too large, constraints might not be satisfied anywhere.

STRIDE = 1.0

if not hasattr(TestFunctionClass, "dim"):
    TestFunction = TestFunctionClass(dim=DIMENSION)
else:
    TestFunction = TestFunctionClass()
    DIMENSION = TestFunctionClass().dim

BOUNDS = TestFunction.bounds
WRAPPED_FUNCTION = botorch_function_wrapper(test_function=TestFunction)

Creating the searchspace and the objective

Since the searchspace is continuous, we construct NumericalContinuousParameter. We use the data of the test function to deduce bounds and number of parameters.

parameters = [
    NumericalDiscreteParameter(
        name=f"x_{k + 1}",
        values=np.arange(
            np.round(BOUNDS[0, k], 0),
            np.round(BOUNDS[1, k], 0) + STRIDE,
            STRIDE,
        ).tolist(),
    )
    for k in range(0, DIMENSION // 2)
] + [
    NumericalContinuousParameter(
        name=f"x_{k+1}",
        bounds=(BOUNDS[0, k], BOUNDS[1, k]),
    )
    for k in range(DIMENSION // 2, DIMENSION)
]

We model the following constraints:

• \(1.0*x_1 + 1.0*x_2 = 1.0\)

• \(1.0*x_3 - 1.0*x_4 = 2.0\)

constraints = [
    DiscreteSumConstraint(
        parameters=["x_1", "x_2"],
        condition=ThresholdCondition(
            threshold=1.0, operator="==", tolerance=STRIDE / 2.0
        ),
    ),
    ContinuousLinearEqualityConstraint(
        parameters=["x_3", "x_4"], coefficients=[1.0, -1.0], rhs=2.0
    ),
]

searchspace = SearchSpace.from_product(parameters=parameters, constraints=constraints)
objective = SingleTargetObjective(target=NumericalTarget(name="Target", mode="MIN"))

Construct the campaign and run some iterations

campaign = Campaign(
    searchspace=searchspace,
    objective=objective,
)

BATCH_SIZE = 5
N_ITERATIONS = 2

for k in range(N_ITERATIONS):
    recommendation = campaign.recommend(batch_size=BATCH_SIZE)

    # target value are looked up via the botorch wrapper
    target_values = []
    for index, row in recommendation.iterrows():
        target_values.append(WRAPPED_FUNCTION(*row.to_list()))

    recommendation["Target"] = target_values

    campaign.add_measurements(recommendation)

### Verify the constraints
measurements = campaign.measurements
TOLERANCE = 0.01

\(1.0*x_1 + 1.0*x_2 = 1.0\)

print(
    "1.0*x_1 + 1.0*x_2 = 1.0 satisfied in all recommendations? ",
    np.allclose(
        1.0 * measurements["x_1"] + 1.0 * measurements["x_2"], 1.0, atol=TOLERANCE
    ),
)

1.0*x_1 + 1.0*x_2 = 1.0 satisfied in all recommendations?  True

\(1.0*x_3 - 1.0*x_4 = 2.0\)

print(
    "1.0*x_3 - 1.0*x_4 = 2.0 satisfied in all recommendations? ",
    np.allclose(
        1.0 * measurements["x_3"] - 1.0 * measurements["x_4"], 2.0, atol=TOLERANCE
    ),
)

1.0*x_3 - 1.0*x_4 = 2.0 satisfied in all recommendations?  True