Bayesian optimization with fixed features¶

In some contexts a variable/feature needs to be fixed during optimization. However, we can leverage previous measurements near the fixed variable value to potentially jump-start optimization using observed model covariances established by the GP kernel . In this example, we start with a number of random observations in 2D input space and then proceed with BO at a fixed value for one of the variables. This notebook uses the 2D Rosenbrock test function as an example. Note that because we are optimizing 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 xopt.generators.bayesian.visualize import plot_model_prediction
from xopt import Xopt, Evaluator
from xopt.generators.bayesian import UpperConfidenceBoundGenerator
from xopt.resources.test_functions.rosenbrock import (
    evaluate_rosenbrock,
    make_rosenbrock_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

# make rosenbrock function vocs in 2D
vocs = make_rosenbrock_vocs(2)

# define a fixed value for the BO generator
fixed_features = {"x0": -1.0}
generator = UpperConfidenceBoundGenerator(vocs=vocs, fixed_features=fixed_features)
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_rosenbrock)

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

# set values if testing import os from xopt.generators.bayesian.visualize import plot_model_prediction from xopt import Xopt, Evaluator from xopt.generators.bayesian import UpperConfidenceBoundGenerator from xopt.resources.test_functions.rosenbrock import ( evaluate_rosenbrock, make_rosenbrock_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 # make rosenbrock function vocs in 2D vocs = make_rosenbrock_vocs(2) # define a fixed value for the BO generator fixed_features = {"x0": -1.0} generator = UpperConfidenceBoundGenerator(vocs=vocs, fixed_features=fixed_features) 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_rosenbrock) 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.rosenbrock.evaluate_rosenbrock
  function_kwargs:
    dummy: 1
    label: y
  max_workers: 1
  vectorized: false
generator:
  beta: 2.0
  computation_time: null
  custom_objective: null
  fixed_features:
    x0: -1.0
  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: null
  model: null
  n_candidates: 1
  n_interpolate_points: null
  n_monte_carlo_samples: 128
  name: upper_confidence_bound
  numerical_optimizer:
    max_iter: 2000
    max_time: 5.0
    n_restarts: 20
    name: LBFGS
  supports_batch_generation: true
  supports_constraints: true
  supports_single_objective: true
  turbo_controller: null
  use_cuda: false
max_evaluations: null
serialize_inline: false
serialize_torch: false
strict: true
vocs:
  constants: {}
  constraints: {}
  objectives:
    y: MINIMIZE
  observables: []
  variables:
    x0:
    - -2.0
    - 2.0
    x1:
    - -2.0
    - 2.0

Generate some initial random samples in 2D space¶

In [2]:

X.random_evaluate(10)

X.random_evaluate(10)

Out[2]:

	x0	x1	y	xopt_runtime	xopt_error
0	1.822762	-0.715318	1631.041468	0.000007	False
1	1.594683	1.152906	193.593565	0.000004	False
2	0.432707	-0.510571	49.015205	0.000003	False
3	-0.675611	0.990674	31.347154	0.000002	False
4	-1.461406	0.165948	394.053685	0.000002	False
5	1.925545	-1.567639	2783.799728	0.000002	False
6	1.081800	0.379565	62.531409	0.000002	False
7	0.222229	-0.119671	3.462950	0.000002	False
8	-0.982458	-0.205924	141.088909	0.000002	False
9	1.339336	1.661679	1.861292	0.000002	False

Run BO steps with fixed features¶

In [3]:

for i in range(5):
    X.step()

for i in range(5): X.step()

In [4]:

X.data

X.data

Out[4]:

	x0	x1	y	xopt_runtime	xopt_error
0	1.822762	-0.715318	1631.041468	0.000007	False
1	1.594683	1.152906	193.593565	0.000004	False
2	0.432707	-0.510571	49.015205	0.000003	False
3	-0.675611	0.990674	31.347154	0.000002	False
4	-1.461406	0.165948	394.053685	0.000002	False
5	1.925545	-1.567639	2783.799728	0.000002	False
6	1.081800	0.379565	62.531409	0.000002	False
7	0.222229	-0.119671	3.462950	0.000002	False
8	-0.982458	-0.205924	141.088909	0.000002	False
9	1.339336	1.661679	1.861292	0.000002	False
10	-1.000000	-2.000000	904.000000	0.000008	False
11	-1.000000	2.000000	104.000000	0.000006	False
12	-1.000000	2.000000	104.000000	0.000006	False
13	-1.000000	0.989894	4.010212	0.000006	False
14	-1.000000	0.719945	11.843089	0.000006	False

Visualize model and evaluations¶

Note that for the BO samples, they all are on the line $x_0=-1$

In [5]:

ax = plot_model_prediction(
    model=X.generator.model,
    vocs=X.vocs,
    data=X.data,
    show_samples=False,
    n_grid=100,
)
ax.plot(
    *X.data[["x0", "x1"]].to_numpy()[:10].T, "+C1", label="random samples", zorder=10
)
ax.plot(*X.data[["x0", "x1"]].to_numpy()[10:].T, "+C3", label="GP samples", zorder=10)
ax.axvline(-1.0, ls="--")
ax.legend();

ax = plot_model_prediction( model=X.generator.model, vocs=X.vocs, data=X.data, show_samples=False, n_grid=100, ) ax.plot( *X.data[["x0", "x1"]].to_numpy()[:10].T, "+C1", label="random samples", zorder=10 ) ax.plot(*X.data[["x0", "x1"]].to_numpy()[10:].T, "+C3", label="GP samples", zorder=10) ax.axvline(-1.0, ls="--") ax.legend();

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[5], line 1
----> 1 ax = plot_model_prediction(
      2     model=X.generator.model,
      3     vocs=X.vocs,
      4     data=X.data,
      5     show_samples=False,
      6     n_grid=100,
      7 )
      8 ax.plot(
      9     *X.data[["x0", "x1"]].to_numpy()[:10].T, "+C1", label="random samples", zorder=10
     10 )
     11 ax.plot(*X.data[["x0", "x1"]].to_numpy()[10:].T, "+C3", label="GP samples", zorder=10)

TypeError: plot_model_prediction() missing 1 required positional argument: 'tkwargs'

Run with fixed feature that is not in vocs¶

We can also run fixed features where the fixed variable is not listed in vocs, as long as the generator data contains data corresponding to the fixed feature name. To satisfy this requirements we add the data from the last optimization run.

In [6]:

# make rosenbrock function vocs in 2-D but remove the `x0` name (set to a fixed
# feature in the next cell)
vocs = make_rosenbrock_vocs(2)
vocs.variables = {"x1": [-2.0, 2.0]}

# make rosenbrock function vocs in 2-D but remove the `x0` name (set to a fixed # feature in the next cell) vocs = make_rosenbrock_vocs(2) vocs.variables = {"x1": [-2.0, 2.0]}

In [7]:

# define a fixed value for the BO generator
fixed_features = {"x0": -1.0}
generator = UpperConfidenceBoundGenerator(vocs=vocs, fixed_features=fixed_features)
generator.numerical_optimizer.n_restarts = NUM_RESTARTS
generator.n_monte_carlo_samples = NUM_MC_SAMPLES

evaluator = Evaluator(function=evaluate_rosenbrock)

X2 = Xopt(generator=generator, evaluator=evaluator, vocs=vocs)
X2.add_data(X.data)

# define a fixed value for the BO generator fixed_features = {"x0": -1.0} generator = UpperConfidenceBoundGenerator(vocs=vocs, fixed_features=fixed_features) generator.numerical_optimizer.n_restarts = NUM_RESTARTS generator.n_monte_carlo_samples = NUM_MC_SAMPLES evaluator = Evaluator(function=evaluate_rosenbrock) X2 = Xopt(generator=generator, evaluator=evaluator, vocs=vocs) X2.add_data(X.data)

In [8]:

# run an optimization step
X2.step()

# run an optimization step X2.step()

In [9]:

X2.data

X2.data

Out[9]:

	x0	x1	y	xopt_runtime	xopt_error
0	1.822762	-0.715318	1631.041468	0.000007	False
1	1.594683	1.152906	193.593565	0.000004	False
2	0.432707	-0.510571	49.015205	0.000003	False
3	-0.675611	0.990674	31.347154	0.000002	False
4	-1.461406	0.165948	394.053685	0.000002	False
5	1.925545	-1.567639	2783.799728	0.000002	False
6	1.081800	0.379565	62.531409	0.000002	False
7	0.222229	-0.119671	3.462950	0.000002	False
8	-0.982458	-0.205924	141.088909	0.000002	False
9	1.339336	1.661679	1.861292	0.000002	False
10	-1.000000	-2.000000	904.000000	0.000008	False
11	-1.000000	2.000000	104.000000	0.000006	False
12	-1.000000	2.000000	104.000000	0.000006	False
13	-1.000000	0.989894	4.010212	0.000006	False
14	-1.000000	0.719945	11.843089	0.000006	False
15	-1.000000	1.119363	5.424750	0.000007	False