This tutorial illustrates the core visualization utilities available in Ax.
import numpy as np
from ax.service.ax_client import AxClient
from ax.modelbridge.cross_validation import cross_validate
from ax.plot.contour import interact_contour
from ax.plot.diagnostic import interact_cross_validation
from ax.plot.scatter import(
interact_fitted,
plot_objective_vs_constraints,
tile_fitted,
)
from ax.plot.slice import plot_slice
from ax.utils.measurement.synthetic_functions import hartmann6
from ax.utils.notebook.plotting import render, init_notebook_plotting
init_notebook_plotting()
[INFO 08-17 19:19:00] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.
The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials
noise_sd = 0.1
param_names = [f"x{i+1}" for i in range(6)] # x1, x2, ..., x6
def noisy_hartmann_evaluation_function(parameterization):
x = np.array([parameterization.get(p_name) for p_name in param_names])
noise1, noise2 = np.random.normal(0, noise_sd, 2)
return {
"hartmann6": (hartmann6(x) + noise1, noise_sd),
"l2norm": (np.sqrt((x ** 2).sum()) + noise2, noise_sd)
}
ax_client = AxClient()
ax_client.create_experiment(
name="test_visualizations",
parameters=[
{
"name": p_name,
"type": "range",
"bounds": [0.0, 1.0],
}
for p_name in param_names
],
objective_name="hartmann6",
minimize=True,
outcome_constraints=["l2norm <= 1.25"]
)
[INFO 08-17 19:19:00] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 6 decimal points.
[INFO 08-17 19:19:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 08-17 19:19:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 08-17 19:19:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 08-17 19:19:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 08-17 19:19:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 08-17 19:19:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 08-17 19:19:00] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x1', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x2', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x3', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x4', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x5', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x6', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[]).
[INFO 08-17 19:19:00] ax.modelbridge.dispatch_utils: Using Bayesian optimization since there are more ordered parameters than there are categories for the unordered categorical parameters.
[INFO 08-17 19:19:00] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 12 trials, GPEI for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.
for i in range(20):
parameters, trial_index = ax_client.get_next_trial()
# Local evaluation here can be replaced with deployment to external system.
ax_client.complete_trial(trial_index=trial_index, raw_data=noisy_hartmann_evaluation_function(parameters))
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.522791, 'x2': 0.096022, 'x3': 0.702384, 'x4': 0.399222, 'x5': 0.455364, 'x6': 0.5209}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.829457, 0.1), 'l2norm': (1.183387, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.773745, 'x2': 0.093092, 'x3': 0.247222, 'x4': 0.585888, 'x5': 0.294476, 'x6': 0.473888}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.217803, 0.1), 'l2norm': (0.971702, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.705933, 'x2': 0.801833, 'x3': 0.177404, 'x4': 0.063342, 'x5': 0.193942, 'x6': 0.4848}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (0.006422, 0.1), 'l2norm': (1.268999, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.767577, 'x2': 0.789208, 'x3': 0.518632, 'x4': 0.881343, 'x5': 0.251359, 'x6': 0.098381}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.007809, 0.1), 'l2norm': (1.555475, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.341758, 'x2': 0.789893, 'x3': 0.196094, 'x4': 0.711278, 'x5': 0.840694, 'x6': 0.089609}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-2.108118, 0.1), 'l2norm': (1.363439, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.409433, 'x2': 0.014088, 'x3': 0.359825, 'x4': 0.806296, 'x5': 0.236295, 'x6': 0.84097}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.395754, 0.1), 'l2norm': (1.437141, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.750118, 'x2': 0.531973, 'x3': 0.565425, 'x4': 0.038888, 'x5': 0.886027, 'x6': 0.261148}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.05925, 0.1), 'l2norm': (1.466117, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.03576, 'x2': 0.562891, 'x3': 0.715227, 'x4': 0.90437, 'x5': 0.964702, 'x6': 0.731611}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (0.020015, 0.1), 'l2norm': (1.723995, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.765221, 'x2': 0.352615, 'x3': 0.872664, 'x4': 0.945797, 'x5': 0.147564, 'x6': 0.856606}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.736025, 0.1), 'l2norm': (1.778332, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.341896, 'x2': 0.195082, 'x3': 0.592587, 'x4': 0.365684, 'x5': 0.463302, 'x6': 0.243977}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.457662, 0.1), 'l2norm': (0.986625, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.130236, 'x2': 0.223543, 'x3': 0.612237, 'x4': 0.636673, 'x5': 0.197371, 'x6': 0.522296}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.64073, 0.1), 'l2norm': (0.932836, 0.1)}.
[INFO 08-17 19:19:00] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.201369, 'x2': 0.707901, 'x3': 0.576174, 'x4': 0.944329, 'x5': 0.413604, 'x6': 0.471734}.
[INFO 08-17 19:19:00] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (0.060777, 0.1), 'l2norm': (1.329567, 0.1)}.
[INFO 08-17 19:19:21] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.3098, 'x2': 0.650513, 'x3': 0.18376, 'x4': 0.631801, 'x5': 0.793063, 'x6': 0.143278}.
[INFO 08-17 19:19:21] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.371506, 0.1), 'l2norm': (1.181631, 0.1)}.
[INFO 08-17 19:19:58] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.308657, 'x2': 0.781304, 'x3': 0.177742, 'x4': 0.613493, 'x5': 0.82053, 'x6': 0.175047}.
[INFO 08-17 19:19:58] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.969521, 0.1), 'l2norm': (1.305342, 0.1)}.
[INFO 08-17 19:20:28] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.298929, 'x2': 0.800135, 'x3': 0.183083, 'x4': 0.532869, 'x5': 0.827715, 'x6': 0.041594}.
[INFO 08-17 19:20:28] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-2.347299, 0.1), 'l2norm': (1.477436, 0.1)}.
[INFO 08-17 19:21:18] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.164342, 'x2': 0.7734, 'x3': 0.153013, 'x4': 0.731503, 'x5': 0.782775, 'x6': 0.119114}.
[INFO 08-17 19:21:18] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-0.63831, 0.1), 'l2norm': (1.382603, 0.1)}.
[INFO 08-17 19:21:46] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.34942, 'x2': 0.744105, 'x3': 0.219218, 'x4': 0.506657, 'x5': 0.722175, 'x6': 0.217414}.
[INFO 08-17 19:21:46] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.383296, 0.1), 'l2norm': (1.200137, 0.1)}.
[INFO 08-17 19:22:45] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.324248, 'x2': 0.768131, 'x3': 0.104987, 'x4': 0.496743, 'x5': 0.895188, 'x6': 0.205844}.
[INFO 08-17 19:22:45] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-1.58982, 0.1), 'l2norm': (1.431029, 0.1)}.
[INFO 08-17 19:23:45] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.312934, 'x2': 0.806893, 'x3': 0.134982, 'x4': 0.64607, 'x5': 0.653212, 'x6': 0.091338}.
[INFO 08-17 19:23:45] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.312109, 0.1), 'l2norm': (1.189659, 0.1)}.
[INFO 08-17 19:24:22] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.31148, 'x2': 0.783801, 'x3': 0.200755, 'x4': 0.540033, 'x5': 0.528807, 'x6': 0.062417}.
[INFO 08-17 19:24:22] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.267889, 0.1), 'l2norm': (1.045947, 0.1)}.
The plot below shows the response surface for hartmann6 metric as a function of the x1, x2 parameters.
The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them.
# this could alternately be done with `ax.plot.contour.plot_contour`
render(ax_client.get_contour_plot(param_x="x1", param_y="x2", metric_name='hartmann6'))
[INFO 08-17 19:24:22] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.
The plot below allows toggling between different pairs of parameters to view the contours.
model = ax_client.generation_strategy.model
render(interact_contour(model=model, metric_name='hartmann6'))
This plot illustrates the tradeoffs achievable for 2 different metrics. The plot takes the x-axis metric as input (usually the objective) and allows toggling among all other metrics for the y-axis.
This is useful to get a sense of the pareto frontier (i.e. what is the best objective value achievable for different bounds on the constraint)
render(plot_objective_vs_constraints(model, 'hartmann6', rel=False))
CV plots are useful to check how well the model predictions calibrate against the actual measurements. If all points are close to the dashed line, then the model is a good predictor of the real data.
cv_results = cross_validate(model)
render(interact_cross_validation(cv_results))
Slice plots show the metric outcome as a function of one parameter while fixing the others. They serve a similar function as contour plots.
render(plot_slice(model, "x2", "hartmann6"))
Tile plots are useful for viewing the effect of each arm.
render(interact_fitted(model, rel=False))
Total runtime of script: 5 minutes, 39.88 seconds.