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. Note that because we are exploring a problem with no noise we set use_low_noise_prior=True in the GP model constructor.

In [1]:

# 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
generator.gp_constructor.use_low_noise_prior = True

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 generator.gp_constructor.use_low_noise_prior = True evaluator = Evaluator(function=evaluate_TNK) X = Xopt(generator=generator, evaluator=evaluator, vocs=vocs) X

Out[1]:

            Xopt
________________________________
Version: 2.6.7.dev55+g7aa2f3618.d20250930
Data size: 0
Config as YAML:
dump_file: null
evaluator:
  function: xopt.resources.test_functions.tnk.evaluate_TNK
  function_kwargs:
    raise_probability: 0
    random_sleep: 0
    sleep: 0
  max_workers: 1
  vectorized: false
generator:
  computation_time: null
  custom_objective: null
  fixed_features: null
  gp_constructor:
    covar_modules: {}
    custom_noise_prior: null
    mean_modules: {}
    name: standard
    trainable_mean_keys: []
    transform_inputs: true
    use_cached_hyperparameters: false
    use_low_noise_prior: true
  max_travel_distances:
  - 0.25
  - 0.25
  model: null
  n_candidates: 1
  n_interpolate_points: null
  n_monte_carlo_samples: 128
  name: bayesian_exploration
  numerical_optimizer:
    max_iter: 2000
    max_time: 5.0
    n_restarts: 20
    name: LBFGS
  supports_batch_generation: true
  supports_constraints: true
  turbo_controller: null
  use_cuda: false
max_evaluations: null
serialize_inline: false
serialize_torch: false
strict: true
vocs:
  constants:
    a: dummy_constant
  constraints:
    c1:
    - GREATER_THAN
    - 0.0
    c2:
    - LESS_THAN
    - 0.5
  objectives: {}
  observables:
  - y1
  variables:
    x1:
    - 0.0
    - 3.14159
    x2:
    - 0.0
    - 3.14159

Run exploration¶

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

In [2]:

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]})

Out[2]:

	x1	x2	a	y1	y2	c1	c2	xopt_runtime	xopt_error
0	1.00	0.70	dummy_constant	1.00	0.70	0.584045	0.290	0.000158	False
1	0.75	0.95	dummy_constant	0.75	0.95	0.494833	0.265	0.000134	False

In [3]:

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

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

step 0

step 1

In [4]:

# view the data
X.data

# view the data X.data

Out[4]:

	x1	x2	a	y1	y2	c1	c2	xopt_runtime	xopt_error
0	1.000000	0.700000	dummy_constant	1.000000	0.700000	0.584045	0.290000	0.000158	False
1	0.750000	0.950000	dummy_constant	0.750000	0.950000	0.494833	0.265000	0.000134	False
2	0.000000	0.164602	dummy_constant	0.000000	0.164602	-1.072906	0.362491	0.000149	False
3	0.785397	0.008041	dummy_constant	0.785397	0.008041	-0.481748	0.323476	0.000149	False

In [5]:

# 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.

In [6]:

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¶

In [7]:

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

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

models.0.likelihood.noise_covar.raw_noise:Parameter containing:
tensor([-22.5689], dtype=torch.float64, requires_grad=True)
models.0.mean_module.raw_constant:Parameter containing:
tensor(-0.2911, dtype=torch.float64, requires_grad=True)
models.0.covar_module.raw_lengthscale:Parameter containing:
tensor([[0.2037, 0.3774]], dtype=torch.float64, requires_grad=True)
models.1.likelihood.noise_covar.raw_noise:Parameter containing:
tensor([-23.3103], dtype=torch.float64, requires_grad=True)
models.1.mean_module.raw_constant:Parameter containing:
tensor(0.1427, dtype=torch.float64, requires_grad=True)
models.1.covar_module.raw_lengthscale:Parameter containing:
tensor([[0.6330, 0.1772]], dtype=torch.float64, requires_grad=True)
models.2.likelihood.noise_covar.raw_noise:Parameter containing:
tensor([-23.4274], dtype=torch.float64, requires_grad=True)
models.2.mean_module.raw_constant:Parameter containing:
tensor(-0.0952, dtype=torch.float64, requires_grad=True)
models.2.covar_module.raw_lengthscale:Parameter containing:
tensor([[0.2152, 0.6472]], dtype=torch.float64, requires_grad=True)

Out[7]:

Parameter containing:
tensor([[0.2152, 0.6472]], dtype=torch.float64, requires_grad=True)

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 [8]:

X.vocs.feasibility_data(X.data)

X.vocs.feasibility_data(X.data)

Out[8]:

	feasible_c1	feasible_c2	feasible
0	True	True	True
1	True	True	True
2	False	True	False
3	False	True	False

In [9]:

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

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

Out[9]:

[{'x1': 1.570795, 'x2': 0.6066689539639962}]