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.

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
from xopt.vocs import get_feasibility_data

# 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 = {"y1": "EXPLORE"}

generator = BayesianExplorationGenerator(vocs=vocs)
generator.numerical_optimizer.n_restarts = NUM_RESTARTS
generator.numerical_optimizer.max_iter = 100
generator.n_monte_carlo_samples = NUM_MC_SAMPLES
generator.n_interpolate_points = 5

evaluator = Evaluator(function=evaluate_TNK)

X = Xopt(generator=generator, evaluator=evaluator)
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 from xopt.vocs import get_feasibility_data # 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 = {"y1": "EXPLORE"} generator = BayesianExplorationGenerator(vocs=vocs) generator.numerical_optimizer.n_restarts = NUM_RESTARTS generator.numerical_optimizer.max_iter = 100 generator.n_monte_carlo_samples = NUM_MC_SAMPLES generator.n_interpolate_points = 5 evaluator = Evaluator(function=evaluate_TNK) X = Xopt(generator=generator, evaluator=evaluator) X

Out[1]:

            Xopt
________________________________
Version: 0.1.dev1+g210ad3716
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
    train_config: null
    train_kwargs: null
    train_method: lbfgs
    train_model: true
    trainable_mean_keys: []
    transform_inputs: true
    use_cached_hyperparameters: false
    use_low_noise_prior: false
  max_travel_distances: null
  model: null
  n_candidates: 1
  n_interpolate_points: 5
  n_monte_carlo_samples: 128
  name: bayesian_exploration
  numerical_optimizer:
    discrete_max_batch_size: 2048
    discrete_max_choices: 4096
    max_iter: 100
    max_time: 5.0
    mixed_max_discrete_configurations: 512
    n_restarts: 20
    name: LBFGS
  returns_id: false
  supports_batch_generation: true
  supports_constraints: true
  supports_discrete_variables: true
  supports_multi_objective: true
  supports_single_objective: true
  turbo_controller: null
  use_cuda: false
  vocs:
    constants:
      a:
        dtype: null
        type: Constant
        value: dummy_constant
    constraints:
      c1:
        dtype: null
        type: GreaterThanConstraint
        value: 0.0
      c2:
        dtype: null
        type: LessThanConstraint
        value: 0.5
    objectives:
      y1:
        dtype: null
        type: ExploreObjective
    observables: {}
    variables:
      x1:
        default_value: null
        domain:
        - 0.0
        - 3.14159
        dtype: null
        type: ContinuousVariable
      x2:
        default_value: null
        domain:
        - 0.0
        - 3.14159
        dtype: null
        type: ContinuousVariable
serialize_inline: false
serialize_torch: false
stopping_condition: null
strict: true

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	0.003915	False
1	0.75	0.95	dummy_constant	0.75	0.95	0.494833	0.265	0.000146	False

In [3]:

for i in range(20):
    print(f"step {i}")
    X.step()

for i in range(20): print(f"step {i}") X.step()

step 0

step 1

step 2

step 3

step 4

step 5

step 6

step 7

step 8

step 9

step 10

step 11

step 12

step 13

step 14

step 15

step 16

step 17

step 18

step 19

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	0.003915	False
1	0.750000	0.950000	dummy_constant	0.750000	0.950000	0.494833	0.265000	0.000146	False
2	1.228318	1.388318	dummy_constant	1.228318	1.388318	2.380252	1.319556	0.013650	False
3	1.706636	1.826636	dummy_constant	1.706636	1.826636	5.163599	3.215934	0.005981	False
4	2.184954	2.264954	dummy_constant	2.184954	2.264954	8.808148	5.954133	0.000160	False
...	...	...	...	...	...	...	...	...	...
97	0.246362	0.833021	dummy_constant	0.246362	0.833021	-0.234245	0.175235	0.000156	False
98	0.443210	0.641547	dummy_constant	0.443210	0.641547	-0.295045	0.023261	0.000140	False
99	0.640058	0.450073	dummy_constant	0.640058	0.450073	-0.294926	0.022109	0.000099	False
100	0.836906	0.258599	dummy_constant	0.836906	0.258599	-0.240967	0.171780	0.000132	False
101	1.033754	0.067125	dummy_constant	1.033754	0.067125	0.022313	0.472274	0.000131	False

102 rows × 9 columns

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([0.0001], requires_grad=True)
models.0.mean_module.raw_constant:Parameter containing:
tensor(1.4424, requires_grad=True)
models.0.covar_module.raw_lengthscale:Parameter containing:
tensor([[0.6808, 7.8367]], requires_grad=True)
models.1.likelihood.noise_covar.raw_noise:Parameter containing:
tensor([0.0002], requires_grad=True)
models.1.mean_module.raw_constant:Parameter containing:
tensor(2.1180, requires_grad=True)
models.1.covar_module.raw_lengthscale:Parameter containing:
tensor([[0.4557, 0.3229]], requires_grad=True)
models.2.likelihood.noise_covar.raw_noise:Parameter containing:
tensor([0.0001], requires_grad=True)
models.2.mean_module.raw_constant:Parameter containing:
tensor(3.6843, requires_grad=True)
models.2.covar_module.raw_lengthscale:Parameter containing:
tensor([[0.5733, 0.5500]], requires_grad=True)

Out[7]:

Parameter containing:
tensor([[0.5733, 0.5500]], 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]:

get_feasibility_data(X.vocs, X.data)

get_feasibility_data(X.vocs, X.data)

Out[8]:

	feasible_c1	feasible_c2	feasible
0	True	True	True
1	True	True	True
2	True	False	False
3	True	False	False
4	True	False	False
...	...	...	...
97	False	True	False
98	False	True	False
99	False	True	False
100	False	True	False
101	True	True	True

102 rows × 3 columns

In [9]:

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

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

Out[9]:

[{'x1': 1.033461535009296, 'x2': 0.06667547223958985},
 {'x1': 1.0331692739579357, 'x2': 0.06622613794857253},
 {'x1': 1.0328770129065752, 'x2': 0.06577680365755523},
 {'x1': 1.032584751855215, 'x2': 0.06532746936653791},
 {'x1': 1.0322924908038544, 'x2': 0.0648781350755206}]