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 09-15 02:37:53] 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 09-15 02:37:53] 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 2 decimal points.
[INFO 09-15 02:37:53] 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 09-15 02:37:53] 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 09-15 02:37:53] 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 09-15 02:37:53] 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 09-15 02:37:53] 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 09-15 02:37:53] 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 09-15 02:37:53] ax.modelbridge.dispatch_utils: Using Bayesian optimization since there are more ordered parameters than there are categories for the unordered categorical parameters.
[INFO 09-15 02:37:53] 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 09-15 02:37:53] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.2, 'x2': 0.01, 'x3': 0.87, 'x4': 0.47, 'x5': 0.74, 'x6': 0.4}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.03, 0.1), 'l2norm': (1.29, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.74, 'x2': 0.7, 'x3': 0.01, 'x4': 0.68, 'x5': 0.95, 'x6': 0.66}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.01, 0.1), 'l2norm': (1.68, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.84, 'x2': 0.57, 'x3': 0.17, 'x4': 0.82, 'x5': 0.99, 'x6': 0.49}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (0.02, 0.1), 'l2norm': (1.67, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.79, 'x2': 0.25, 'x3': 0.55, 'x4': 0.45, 'x5': 0.32, 'x6': 0.52}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.43, 0.1), 'l2norm': (1.19, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.73, 'x2': 0.72, 'x3': 0.94, 'x4': 0.94, 'x5': 0.09, 'x6': 0.15}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.04, 0.1), 'l2norm': (1.59, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.81, 'x2': 0.17, 'x3': 0.21, 'x4': 0.36, 'x5': 0.88, 'x6': 0.47}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.2, 0.1), 'l2norm': (1.52, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.81, 'x2': 0.57, 'x3': 0.41, 'x4': 0.54, 'x5': 0.57, 'x6': 0.89}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.14, 0.1), 'l2norm': (1.77, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.46, 'x2': 0.28, 'x3': 0.07, 'x4': 0.34, 'x5': 0.53, 'x6': 0.75}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.71, 0.1), 'l2norm': (0.91, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.22, 'x2': 0.13, 'x3': 0.45, 'x4': 0.98, 'x5': 0.49, 'x6': 0.34}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (0.05, 0.1), 'l2norm': (1.14, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.03, 'x2': 0.14, 'x3': 0.05, 'x4': 0.96, 'x5': 0.37, 'x6': 0.03}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (0.01, 0.1), 'l2norm': (1.0, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.52, 'x2': 0.9, 'x3': 0.7, 'x4': 0.55, 'x5': 0.83, 'x6': 0.66}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (0.0, 0.1), 'l2norm': (1.57, 0.1)}.
[INFO 09-15 02:37:53] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.07, 'x2': 0.06, 'x3': 0.33, 'x4': 0.81, 'x5': 0.7, 'x6': 0.43}.
[INFO 09-15 02:37:53] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.08, 0.1), 'l2norm': (1.12, 0.1)}.
[INFO 09-15 02:38:07] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.51, 'x2': 0.25, 'x3': 0.15, 'x4': 0.32, 'x5': 0.43, 'x6': 0.71}.
[INFO 09-15 02:38:07] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.54, 0.1), 'l2norm': (1.17, 0.1)}.
[INFO 09-15 02:38:09] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.43, 'x2': 0.23, 'x3': 0.17, 'x4': 0.29, 'x5': 0.4, 'x6': 0.69}.
[INFO 09-15 02:38:09] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-2.14, 0.1), 'l2norm': (1.16, 0.1)}.
[INFO 09-15 02:38:15] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.39, 'x2': 0.22, 'x3': 0.18, 'x4': 0.26, 'x5': 0.36, 'x6': 0.68}.
[INFO 09-15 02:38:15] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-2.39, 0.1), 'l2norm': (0.89, 0.1)}.
[INFO 09-15 02:38:17] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.38, 'x2': 0.18, 'x3': 0.21, 'x4': 0.23, 'x5': 0.33, 'x6': 0.65}.
[INFO 09-15 02:38:17] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-2.61, 0.1), 'l2norm': (0.88, 0.1)}.
[INFO 09-15 02:38:20] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.36, 'x2': 0.16, 'x3': 0.22, 'x4': 0.24, 'x5': 0.27, 'x6': 0.7}.
[INFO 09-15 02:38:20] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.64, 0.1), 'l2norm': (1.01, 0.1)}.
[INFO 09-15 02:38:22] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.37, 'x2': 0.23, 'x3': 0.23, 'x4': 0.2, 'x5': 0.26, 'x6': 0.61}.
[INFO 09-15 02:38:22] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.3, 0.1), 'l2norm': (0.81, 0.1)}.
[INFO 09-15 02:38:24] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.34, 'x2': 0.12, 'x3': 0.25, 'x4': 0.22, 'x5': 0.33, 'x6': 0.71}.
[INFO 09-15 02:38:24] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.71, 0.1), 'l2norm': (0.99, 0.1)}.
[INFO 09-15 02:38:26] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.35, 'x2': 0.06, 'x3': 0.18, 'x4': 0.23, 'x5': 0.31, 'x6': 0.68}.
[INFO 09-15 02:38:26] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.58, 0.1), 'l2norm': (0.84, 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 09-15 02:38:26] 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: 1 minutes, 2.74 seconds.