Bayesian Exploration¶

Here we demonstrate the use of Bayesian Exploration to characterize an unknown function in the presence of constraints (see here). The function we wish to explore is the first objective of the TNK test problem.

Specifiying generator options¶

We start with the generator defaults and modify as needed for conservative exploration, which should prevent any constraint violations.

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# set values if testing
import os

from copy import deepcopy
from xopt import Xopt, Evaluator
from xopt.generators.bayesian import BayesianExplorationGenerator
from xopt.resources.test_functions.tnk import evaluate_TNK, tnk_vocs

# Ignore all warnings
import warnings

warnings.filterwarnings("ignore")

SMOKE_TEST = os.environ.get("SMOKE_TEST")
NUM_MC_SAMPLES = 1 if SMOKE_TEST else 128
NUM_RESTARTS = 1 if SMOKE_TEST else 20

vocs = deepcopy(tnk_vocs)
vocs.objectives = {}
vocs.observables = ["y1"]

generator = BayesianExplorationGenerator(vocs=vocs)
generator.max_travel_distances = [0.25, 0.25]
generator.numerical_optimizer.n_restarts = NUM_RESTARTS
generator.n_monte_carlo_samples = NUM_MC_SAMPLES

evaluator = Evaluator(function=evaluate_TNK)

X = Xopt(generator=generator, evaluator=evaluator, vocs=vocs)
X

# set values if testing import os from copy import deepcopy from xopt import Xopt, Evaluator from xopt.generators.bayesian import BayesianExplorationGenerator from xopt.resources.test_functions.tnk import evaluate_TNK, tnk_vocs # Ignore all warnings import warnings warnings.filterwarnings("ignore") SMOKE_TEST = os.environ.get("SMOKE_TEST") NUM_MC_SAMPLES = 1 if SMOKE_TEST else 128 NUM_RESTARTS = 1 if SMOKE_TEST else 20 vocs = deepcopy(tnk_vocs) vocs.objectives = {} vocs.observables = ["y1"] generator = BayesianExplorationGenerator(vocs=vocs) generator.max_travel_distances = [0.25, 0.25] generator.numerical_optimizer.n_restarts = NUM_RESTARTS generator.n_monte_carlo_samples = NUM_MC_SAMPLES evaluator = Evaluator(function=evaluate_TNK) X = Xopt(generator=generator, evaluator=evaluator, vocs=vocs) X

Run exploration¶

We start with evaluating 2 points that we know satisfy the constraints. We then run 30 exploration steps.

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X.evaluate_data({"x1": [1.0, 0.75], "x2": [0.7, 0.95]})

X.evaluate_data({"x1": [1.0, 0.75], "x2": [0.7, 0.95]})

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for i in range(2):
    print(f"step {i}")
    X.step()

for i in range(2): print(f"step {i}") X.step()

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# view the data
X.data

# view the data X.data

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# plot results
ax = X.data.plot("x1", "x2")
ax.set_aspect("equal")

# plot results ax = X.data.plot("x1", "x2") ax.set_aspect("equal")

Introspect models, acquisition function and feasibility prediction¶

During exploration we generate Gaussian Process models of each objective and constraint. We demonstrate how they are viewed below.

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fig, ax = X.generator.visualize_model(show_feasibility=True, n_grid=100)

fig, ax = X.generator.visualize_model(show_feasibility=True, n_grid=100)

Generator model hyperparameters¶

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# print generator model hyperparameters
for name, val in X.generator.model.named_parameters():
    print(f"{name}:{val}")

X.generator.model.models[2].covar_module.base_kernel.lengthscale

# print generator model hyperparameters for name, val in X.generator.model.named_parameters(): print(f"{name}:{val}") X.generator.model.models[2].covar_module.base_kernel.lengthscale

Examine the number of constraint violations¶

Using the convience function provided by the vocs object we can evaluate which samples violate either or both of our constraints.

In [ ]:

X.vocs.feasibility_data(X.data)

X.vocs.feasibility_data(X.data)

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# generate next point
X.generator.generate(1)

# generate next point X.generator.generate(1)