This tutorial illustrates the core visualization utilities available in Ax.
import numpy as np
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.service.ax_client import AxClient, ObjectiveProperties
from ax.utils.measurement.synthetic_functions import hartmann6
from ax.utils.notebook.plotting import init_notebook_plotting, render
init_notebook_plotting()
[INFO 03-01 16:37:19] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.
[INFO 03-01 16:37:19] ax.utils.notebook.plotting: Please see
(https://ax.dev/tutorials/visualizations.html#Fix-for-plots-that-are-not-rendering)
if visualizations are not rendering.
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
],
objectives={"hartmann6": ObjectiveProperties(minimize=True)},
outcome_constraints=["l2norm <= 1.25"],
)
[INFO 03-01 16:37:20] 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 03-01 16:37:20] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 03-01 16:37:20] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 03-01 16:37:20] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 03-01 16:37:20] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 03-01 16:37:20] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 03-01 16:37:20] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.
[INFO 03-01 16:37:20] 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 03-01 16:37:20] ax.modelbridge.dispatch_utils: Using Models.BOTORCH_MODULAR since there is at least one ordered parameter and there are no unordered categorical parameters.
[INFO 03-01 16:37:20] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=6 num_trials=None use_batch_trials=False
[INFO 03-01 16:37:20] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12
[INFO 03-01 16:37:20] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12
[INFO 03-01 16:37:20] ax.modelbridge.dispatch_utils: `verbose`, `disable_progbar`, and `jit_compile` are not yet supported when using `choose_generation_strategy` with ModularBoTorchModel, dropping these arguments.
[INFO 03-01 16:37:20] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+BoTorch', steps=[Sobol for 12 trials, BoTorch 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 03-01 16:37:20] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.405293, 'x2': 0.74935, 'x3': 0.328107, 'x4': 0.67813, 'x5': 0.509819, 'x6': 0.051542} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-2.554969, 0.1), 'l2norm': (1.260087, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.953876, 'x2': 0.27131, 'x3': 0.817712, 'x4': 0.002659, 'x5': 0.169502, 'x6': 0.035105} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (0.118751, 0.1), 'l2norm': (1.262412, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.012144, 'x2': 0.067864, 'x3': 0.526769, 'x4': 0.133143, 'x5': 0.005376, 'x6': 0.773202} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.767316, 0.1), 'l2norm': (0.755229, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.194068, 'x2': 0.344042, 'x3': 0.949107, 'x4': 0.490742, 'x5': 0.933593, 'x6': 0.249598} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (0.06035, 0.1), 'l2norm': (1.489811, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.890174, 'x2': 0.38554, 'x3': 0.493718, 'x4': 0.901018, 'x5': 0.499325, 'x6': 0.801591} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.020413, 0.1), 'l2norm': (1.710817, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.678472, 'x2': 0.083581, 'x3': 0.990709, 'x4': 0.833655, 'x5': 0.662268, 'x6': 0.232551} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.068442, 0.1), 'l2norm': (1.535639, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.978577, 'x2': 0.96843, 'x3': 0.884392, 'x4': 0.899749, 'x5': 0.139095, 'x6': 0.034444} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (0.017722, 0.1), 'l2norm': (1.80642, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.370112, 'x2': 0.632159, 'x3': 0.832172, 'x4': 0.230053, 'x5': 0.931054, 'x6': 0.781986} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.176489, 0.1), 'l2norm': (1.82969, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.183521, 'x2': 0.71696, 'x3': 0.632497, 'x4': 0.284422, 'x5': 0.319276, 'x6': 0.375443} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.739327, 0.1), 'l2norm': (1.307653, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.055582, 'x2': 0.026989, 'x3': 0.642712, 'x4': 0.631488, 'x5': 0.022241, 'x6': 0.920679} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.269545, 0.1), 'l2norm': (1.216927, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.304531, 'x2': 0.89638, 'x3': 0.936778, 'x4': 0.11165, 'x5': 0.071646, 'x6': 0.007822} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.242808, 0.1), 'l2norm': (1.347503, 0.1)}.
[INFO 03-01 16:37:20] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.778506, 'x2': 0.02427, 'x3': 0.603086, 'x4': 0.65902, 'x5': 0.299814, 'x6': 0.659678} using model Sobol.
[INFO 03-01 16:37:20] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.261256, 0.1), 'l2norm': (1.526738, 0.1)}.
[INFO 03-01 16:37:26] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.304189, 'x2': 0.743975, 'x3': 0.320002, 'x4': 0.609169, 'x5': 0.428523, 'x6': 0.06511} using model BoTorch.
[INFO 03-01 16:37:26] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-2.202275, 0.1), 'l2norm': (1.193276, 0.1)}.
[INFO 03-01 16:37:36] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.287856, 'x2': 0.757063, 'x3': 0.286837, 'x4': 0.671959, 'x5': 0.561321, 'x6': 0.0} using model BoTorch.
[INFO 03-01 16:37:36] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.859694, 0.1), 'l2norm': (1.279292, 0.1)}.
[INFO 03-01 16:37:44] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.424433, 'x2': 0.739343, 'x3': 0.3309, 'x4': 0.524169, 'x5': 0.463361, 'x6': 0.066434} using model BoTorch.
[INFO 03-01 16:37:44] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-2.456896, 0.1), 'l2norm': (1.101448, 0.1)}.
[INFO 03-01 16:37:51] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.443945, 'x2': 0.753923, 'x3': 0.338643, 'x4': 0.619732, 'x5': 0.457005, 'x6': 0.087171} using model BoTorch.
[INFO 03-01 16:37:51] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-2.457146, 0.1), 'l2norm': (1.112872, 0.1)}.
[INFO 03-01 16:37:56] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.417616, 'x2': 0.69061, 'x3': 0.36041, 'x4': 0.606034, 'x5': 0.458493, 'x6': 0.016772} using model BoTorch.
[INFO 03-01 16:37:56] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.228838, 0.1), 'l2norm': (1.071268, 0.1)}.
[INFO 03-01 16:38:03] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.425905, 'x2': 0.729397, 'x3': 0.286408, 'x4': 0.619346, 'x5': 0.496688, 'x6': 0.112599} using model BoTorch.
[INFO 03-01 16:38:03] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.432175, 0.1), 'l2norm': (1.125472, 0.1)}.
[INFO 03-01 16:38:08] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.431538, 'x2': 0.818916, 'x3': 0.298256, 'x4': 0.624864, 'x5': 0.464648, 'x6': 0.057468} using model BoTorch.
[INFO 03-01 16:38:08] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.773538, 0.1), 'l2norm': (1.206975, 0.1)}.
[INFO 03-01 16:38:12] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.417722, 'x2': 0.880657, 'x3': 0.323639, 'x4': 0.564667, 'x5': 0.497552, 'x6': 0.071858} using model BoTorch.
[INFO 03-01 16:38:12] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-3.115826, 0.1), 'l2norm': (1.391717, 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 03-01 16:38:12] 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"))