Note
Click here to download the full example code
1. Lightweight, versatile, and platform agnostic architecture
Optuna is entirely written in Python and has few dependencies. This means that we can quickly move to the real example once you get interested in Optuna.
Quadratic Function Example
Usually, Optuna is used to optimize hyperparameters, but as an example, let’s optimize a simple quadratic function: \((x - 2)^2\).
First of all, import optuna.
import optuna
In optuna, conventionally functions to be optimized are named objective.
def objective(trial):
x = trial.suggest_float("x", -10, 10)
return (x - 2) ** 2
This function returns the value of \((x - 2)^2\). Our goal is to find the value of x
that minimizes the output of the objective function. This is the “optimization.”
During the optimization, Optuna repeatedly calls and evaluates the objective function with
different values of x.
A Trial object corresponds to a single execution of the objective
function and is internally instantiated upon each invocation of the function.
The suggest APIs (for example, suggest_float()) are called
inside the objective function to obtain parameters for a trial.
suggest_float() selects parameters uniformly within the range
provided. In our example, from \(-10\) to \(10\).
To start the optimization, we create a study object and pass the objective function to method
optimize() as follows.
study = optuna.create_study()
study.optimize(objective, n_trials=100)
You can get the best parameter as follows.
best_params = study.best_params
found_x = best_params["x"]
print("Found x: {}, (x - 2)^2: {}".format(found_x, (found_x - 2) ** 2))
Found x: 2.015732796129548, (x - 2)^2: 0.00024752087405391804
We can see that the x value found by Optuna is close to the optimal value of 2.
Note
When used to search for hyperparameters in machine learning, usually the objective function would return the loss or accuracy of the model.
Study Object
Let us clarify the terminology in Optuna as follows:
Trial: A single call of the objective function
Study: An optimization session, which is a set of trials
Parameter: A variable whose value is to be optimized, such as
xin the above example
In Optuna, we use the study object to manage optimization.
Method create_study() returns a study object.
A study object has useful properties for analyzing the optimization outcome.
To get the dictionary of parameter name and parameter values:
study.best_params
{'x': 2.015732796129548}
To get the best observed value of the objective function:
study.best_value
0.00024752087405391804
To get the best trial:
study.best_trial
FrozenTrial(number=90, values=[0.00024752087405391804], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 919902), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 923354), params={'x': 2.015732796129548}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=90, state=TrialState.COMPLETE, value=None)
To get all trials:
study.trials
[FrozenTrial(number=0, values=[54.32646914663778], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 606777), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 607205), params={'x': -5.370649167246924}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=0, state=TrialState.COMPLETE, value=None), FrozenTrial(number=1, values=[3.444122244529982], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 607693), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 607977), params={'x': 3.8558346490272193}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=1, state=TrialState.COMPLETE, value=None), FrozenTrial(number=2, values=[11.107850524919385], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 608529), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 608832), params={'x': -1.3328442095182584}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=2, state=TrialState.COMPLETE, value=None), FrozenTrial(number=3, values=[43.878830544105746], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 609337), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 609599), params={'x': -4.624109792576339}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=3, state=TrialState.COMPLETE, value=None), FrozenTrial(number=4, values=[91.74201906158582], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 610007), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 610263), params={'x': -7.578205419679922}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=4, state=TrialState.COMPLETE, value=None), FrozenTrial(number=5, values=[135.33685075877167], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 610802), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 611061), params={'x': -9.633436756125494}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=5, state=TrialState.COMPLETE, value=None), FrozenTrial(number=6, values=[20.648063902205003], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 611473), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 611734), params={'x': -2.5440140737243544}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=6, state=TrialState.COMPLETE, value=None), FrozenTrial(number=7, values=[2.4578854749503614], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 612092), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 612343), params={'x': 0.43223551674674}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=7, state=TrialState.COMPLETE, value=None), FrozenTrial(number=8, values=[118.4884348377346], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 612748), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 613012), params={'x': -8.885239310081088}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=8, state=TrialState.COMPLETE, value=None), FrozenTrial(number=9, values=[132.88753361691246], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 613391), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 613655), params={'x': -9.527685527325616}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=9, state=TrialState.COMPLETE, value=None), FrozenTrial(number=10, values=[61.21513377153766], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 614053), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 617766), params={'x': 9.82401008253042}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=10, state=TrialState.COMPLETE, value=None), FrozenTrial(number=11, values=[2.6651600038199814], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 618221), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 621472), params={'x': 3.632531777277239}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=11, state=TrialState.COMPLETE, value=None), FrozenTrial(number=12, values=[1.5364169481056693], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 622004), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 625192), params={'x': 3.239522871150698}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=12, state=TrialState.COMPLETE, value=None), FrozenTrial(number=13, values=[0.3607428549338023], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 625643), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 628821), params={'x': 2.6006187267591665}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=13, state=TrialState.COMPLETE, value=None), FrozenTrial(number=14, values=[9.5106339557868], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 629290), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 632466), params={'x': 5.083931574433324}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=14, state=TrialState.COMPLETE, value=None), FrozenTrial(number=15, values=[39.864271248075326], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 632920), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 636122), params={'x': 8.313815902295167}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=15, state=TrialState.COMPLETE, value=None), FrozenTrial(number=16, values=[0.7009308615982559], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 636578), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 639768), params={'x': 1.1627838620772675}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=16, state=TrialState.COMPLETE, value=None), FrozenTrial(number=17, values=[0.5551706584050651], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 640221), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 643416), params={'x': 1.2549022490940769}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=17, state=TrialState.COMPLETE, value=None), FrozenTrial(number=18, values=[22.683631151794934], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 643872), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 647086), params={'x': 6.76273357976225}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=18, state=TrialState.COMPLETE, value=None), FrozenTrial(number=19, values=[0.03944601143700113], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 647542), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 650723), params={'x': 1.8013898002694697}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=19, state=TrialState.COMPLETE, value=None), FrozenTrial(number=20, values=[12.032798504668062], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 651204), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 654431), params={'x': -1.4688324411346336}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=20, state=TrialState.COMPLETE, value=None), FrozenTrial(number=21, values=[0.047387824651085306], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 654892), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 658094), params={'x': 1.7823125528398909}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=21, state=TrialState.COMPLETE, value=None), FrozenTrial(number=22, values=[0.04765742048140892], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 658551), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 661796), params={'x': 2.2183057958035217}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=22, state=TrialState.COMPLETE, value=None), FrozenTrial(number=23, values=[16.423056041771037], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 662251), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 665475), params={'x': 6.0525369883285505}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=23, state=TrialState.COMPLETE, value=None), FrozenTrial(number=24, values=[0.14410149780886408], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 665930), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 669153), params={'x': 1.6203929692315169}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=24, state=TrialState.COMPLETE, value=None), FrozenTrial(number=25, values=[5.849339311582978], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 669609), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 672825), params={'x': -0.41854074011230535}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=25, state=TrialState.COMPLETE, value=None), FrozenTrial(number=26, values=[23.818503576188135], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 673310), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 676505), params={'x': -2.880420430269111}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=26, state=TrialState.COMPLETE, value=None), FrozenTrial(number=27, values=[5.180910244613195], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 676963), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 680182), params={'x': 4.276161295825319}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=27, state=TrialState.COMPLETE, value=None), FrozenTrial(number=28, values=[0.1987910409983424], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 680642), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 683941), params={'x': 2.445859889425302}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=28, state=TrialState.COMPLETE, value=None), FrozenTrial(number=29, values=[49.48518326104156], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 684401), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 687682), params={'x': -5.034570581140086}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=29, state=TrialState.COMPLETE, value=None), FrozenTrial(number=30, values=[11.80282983577404], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 688140), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 691424), params={'x': 5.4355246812930975}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=30, state=TrialState.COMPLETE, value=None), FrozenTrial(number=31, values=[0.3231753138819023], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 691882), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 695206), params={'x': 1.4315148956376234}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=31, state=TrialState.COMPLETE, value=None), FrozenTrial(number=32, values=[4.856566009614142], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 695663), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 698958), params={'x': -0.2037617860408919}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=32, state=TrialState.COMPLETE, value=None), FrozenTrial(number=33, values=[0.03629780030703718], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 699415), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 702721), params={'x': 2.1905198160481927}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=33, state=TrialState.COMPLETE, value=None), FrozenTrial(number=34, values=[5.305405490047647], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 703194), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 706463), params={'x': 4.303346584873333}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=34, state=TrialState.COMPLETE, value=None), FrozenTrial(number=35, values=[12.887096075508921], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 706931), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 710235), params={'x': -1.5898601749244943}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=35, state=TrialState.COMPLETE, value=None), FrozenTrial(number=36, values=[30.990277011324896], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 710693), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 713980), params={'x': -3.566891144195734}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=36, state=TrialState.COMPLETE, value=None), FrozenTrial(number=37, values=[0.5849314628846648], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 714439), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 717766), params={'x': 2.7648081216126466}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=37, state=TrialState.COMPLETE, value=None), FrozenTrial(number=38, values=[3.0828416862596986], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 718223), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 721523), params={'x': 0.2441977086642988}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=38, state=TrialState.COMPLETE, value=None), FrozenTrial(number=39, values=[27.9941173995063], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 721981), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 725295), params={'x': 7.290946739432018}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=39, state=TrialState.COMPLETE, value=None), FrozenTrial(number=40, values=[8.460566557401304], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 725754), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 729208), params={'x': -0.9087053060427595}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=40, state=TrialState.COMPLETE, value=None), FrozenTrial(number=41, values=[0.2159645866110809], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 729724), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 732987), params={'x': 1.5352800987572397}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=41, state=TrialState.COMPLETE, value=None), FrozenTrial(number=42, values=[0.011738465046296125], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 733469), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 736764), params={'x': 2.108344197104857}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=42, state=TrialState.COMPLETE, value=None), FrozenTrial(number=43, values=[1.6710162307401555], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 737239), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 740540), params={'x': 0.7073220699879821}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=43, state=TrialState.COMPLETE, value=None), FrozenTrial(number=44, values=[3.096647877497267], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 741004), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 744490), params={'x': 3.759729489864072}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=44, state=TrialState.COMPLETE, value=None), FrozenTrial(number=45, values=[0.17296256677102037], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 744955), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 748341), params={'x': 2.4158876852841646}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=45, state=TrialState.COMPLETE, value=None), FrozenTrial(number=46, values=[8.58907786250055], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 748804), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 752134), params={'x': 4.930712859101101}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=46, state=TrialState.COMPLETE, value=None), FrozenTrial(number=47, values=[1.2488053154582142], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 752596), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 755924), params={'x': 3.1174995818604203}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=47, state=TrialState.COMPLETE, value=None), FrozenTrial(number=48, values=[0.12984608266167647], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 756405), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 759746), params={'x': 2.360341619385933}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=48, state=TrialState.COMPLETE, value=None), FrozenTrial(number=49, values=[74.84815052863901], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 760213), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 763557), params={'x': -6.651482562465176}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=49, state=TrialState.COMPLETE, value=None), FrozenTrial(number=50, values=[17.70755314257785], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 764021), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 767371), params={'x': -2.208034356154647}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=50, state=TrialState.COMPLETE, value=None), FrozenTrial(number=51, values=[0.004927411959763014], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 767837), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 771235), params={'x': 2.0701955266364105}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=51, state=TrialState.COMPLETE, value=None), FrozenTrial(number=52, values=[2.2644881701710653], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 771699), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 775090), params={'x': 0.49517835934916676}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=52, state=TrialState.COMPLETE, value=None), FrozenTrial(number=53, values=[2.222377288369222], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 775553), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 778903), params={'x': 3.490763994859422}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=53, state=TrialState.COMPLETE, value=None), FrozenTrial(number=54, values=[0.022151522733928994], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 779368), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 782711), params={'x': 1.8511661237018635}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=54, state=TrialState.COMPLETE, value=None), FrozenTrial(number=55, values=[7.376725491695942], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 783191), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 786570), params={'x': -0.7160127929919518}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=55, state=TrialState.COMPLETE, value=None), FrozenTrial(number=56, values=[0.07546937001085705], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 787050), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 790401), params={'x': 1.7252831093455354}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=56, state=TrialState.COMPLETE, value=None), FrozenTrial(number=57, values=[5.830776850720715], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 790903), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 794235), params={'x': 4.414700157518675}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=57, state=TrialState.COMPLETE, value=None), FrozenTrial(number=58, values=[1.3218192528545143], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 794703), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 798031), params={'x': 0.8502960151175807}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=58, state=TrialState.COMPLETE, value=None), FrozenTrial(number=59, values=[1.604464718184619], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 798499), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 801870), params={'x': 3.26667466943356}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=59, state=TrialState.COMPLETE, value=None), FrozenTrial(number=60, values=[3.936894980893472], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 802359), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 805709), params={'x': 0.01583897304339943}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=60, state=TrialState.COMPLETE, value=None), FrozenTrial(number=61, values=[0.018937196269456478], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 806178), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 809709), params={'x': 2.137612485877759}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=61, state=TrialState.COMPLETE, value=None), FrozenTrial(number=62, values=[0.01997082710261666], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 810180), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 813537), params={'x': 1.8586818231697824}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=62, state=TrialState.COMPLETE, value=None), FrozenTrial(number=63, values=[1.070104190628223], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 814003), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 817406), params={'x': 0.9655415955060238}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=63, state=TrialState.COMPLETE, value=None), FrozenTrial(number=64, values=[0.0013661821745517377], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 817874), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 821263), params={'x': 1.9630380983369127}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=64, state=TrialState.COMPLETE, value=None), FrozenTrial(number=65, values=[13.922157069545031], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 821733), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 825121), params={'x': 5.731240687699606}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=65, state=TrialState.COMPLETE, value=None), FrozenTrial(number=66, values=[0.7587348688924664], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 825588), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 828955), params={'x': 2.871053884035004}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=66, state=TrialState.COMPLETE, value=None), FrozenTrial(number=67, values=[2.8748854557225862], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 829478), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 832817), params={'x': 3.69554871818022}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=67, state=TrialState.COMPLETE, value=None), FrozenTrial(number=68, values=[0.0009494621524157651], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 833311), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 836658), params={'x': 1.9691866562603835}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=68, state=TrialState.COMPLETE, value=None), FrozenTrial(number=69, values=[0.5911293055596306], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 837169), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 840553), params={'x': 1.2311506613388872}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=69, state=TrialState.COMPLETE, value=None), FrozenTrial(number=70, values=[6.090353045881267], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 841048), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 844434), params={'x': 4.467864065519263}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=70, state=TrialState.COMPLETE, value=None), FrozenTrial(number=71, values=[0.0049273812150574725], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 844908), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 848291), params={'x': 1.9298046923572703}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=71, state=TrialState.COMPLETE, value=None), FrozenTrial(number=72, values=[0.01398824310049944], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 848790), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 852176), params={'x': 1.8817280967410288}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=72, state=TrialState.COMPLETE, value=None), FrozenTrial(number=73, values=[2.910538672490337], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 852647), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 856054), params={'x': 0.2939699086797041}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=73, state=TrialState.COMPLETE, value=None), FrozenTrial(number=74, values=[0.877931950953631], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 856525), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 859920), params={'x': 2.936980229756013}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=74, state=TrialState.COMPLETE, value=None), FrozenTrial(number=75, values=[0.03569559266308607], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 860391), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 863792), params={'x': 2.188932772866663}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=75, state=TrialState.COMPLETE, value=None), FrozenTrial(number=76, values=[5.82292735971962], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 864293), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 867681), params={'x': -0.4130742549121069}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=76, state=TrialState.COMPLETE, value=None), FrozenTrial(number=77, values=[0.7356871930317028], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 868177), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 871578), params={'x': 1.1422779045450078}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=77, state=TrialState.COMPLETE, value=None), FrozenTrial(number=78, values=[0.007472113556798774], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 872076), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 875481), params={'x': 1.9135586120148527}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=78, state=TrialState.COMPLETE, value=None), FrozenTrial(number=79, values=[9.851445292451077], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 875981), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 879406), params={'x': -1.1387012110825518}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=79, state=TrialState.COMPLETE, value=None), FrozenTrial(number=80, values=[9.16547706878296], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 879908), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 883306), params={'x': 5.0274538920986}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=80, state=TrialState.COMPLETE, value=None), FrozenTrial(number=81, values=[3.7931783671928425], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 883811), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 887275), params={'x': 3.9476083711036063}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=81, state=TrialState.COMPLETE, value=None), FrozenTrial(number=82, values=[0.017293428925646368], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 887783), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 891207), params={'x': 1.8684955174693791}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=82, state=TrialState.COMPLETE, value=None), FrozenTrial(number=83, values=[0.46493196046038454], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 891715), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 895171), params={'x': 2.6818591940132395}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=83, state=TrialState.COMPLETE, value=None), FrozenTrial(number=84, values=[1.7049928294922312], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 895694), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 899179), params={'x': 0.6942462600121602}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=84, state=TrialState.COMPLETE, value=None), FrozenTrial(number=85, values=[0.03246580940874488], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 899693), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 903152), params={'x': 2.1801827111815806}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=85, state=TrialState.COMPLETE, value=None), FrozenTrial(number=86, values=[1.6493129982076447], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 903663), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 907097), params={'x': 3.2842558149401717}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=86, state=TrialState.COMPLETE, value=None), FrozenTrial(number=87, values=[0.3376831790014678], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 907603), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 911051), params={'x': 1.4188948640723713}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=87, state=TrialState.COMPLETE, value=None), FrozenTrial(number=88, values=[3.814091949758079], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 911647), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 915440), params={'x': 0.04702996700971385}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=88, state=TrialState.COMPLETE, value=None), FrozenTrial(number=89, values=[0.5762122370905903], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 915950), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 919397), params={'x': 2.75908644902316}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=89, state=TrialState.COMPLETE, value=None), FrozenTrial(number=90, values=[0.00024752087405391804], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 919902), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 923354), params={'x': 2.015732796129548}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=90, state=TrialState.COMPLETE, value=None), FrozenTrial(number=91, values=[0.01565096739313334], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 923865), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 927337), params={'x': 2.125103826452804}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=91, state=TrialState.COMPLETE, value=None), FrozenTrial(number=92, values=[0.67724505154666], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 927840), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 931281), params={'x': 1.1770510030708707}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=92, state=TrialState.COMPLETE, value=None), FrozenTrial(number=93, values=[0.04588878512106828], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 931789), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 935316), params={'x': 1.7857833220286798}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=93, state=TrialState.COMPLETE, value=None), FrozenTrial(number=94, values=[2.067989659853896], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 935822), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 939269), params={'x': 0.5619493542110918}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=94, state=TrialState.COMPLETE, value=None), FrozenTrial(number=95, values=[3.8705287868561555], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 939775), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 943236), params={'x': 3.9673659514325634}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=95, state=TrialState.COMPLETE, value=None), FrozenTrial(number=96, values=[0.29610989189188835], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 943744), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 947263), params={'x': 2.5441598036348223}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=96, state=TrialState.COMPLETE, value=None), FrozenTrial(number=97, values=[1.5275719926389284], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 947768), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 951239), params={'x': 3.235949834191877}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=97, state=TrialState.COMPLETE, value=None), FrozenTrial(number=98, values=[0.21954485352045036], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 951746), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 955216), params={'x': 1.5314438629999065}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=98, state=TrialState.COMPLETE, value=None), FrozenTrial(number=99, values=[0.0032620147435550558], datetime_start=datetime.datetime(2022, 9, 8, 9, 16, 33, 955729), datetime_complete=datetime.datetime(2022, 9, 8, 9, 16, 33, 959213), params={'x': 2.0571140503164944}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=99, state=TrialState.COMPLETE, value=None)]
To get the number of trials:
len(study.trials)
100
By executing optimize() again, we can continue the optimization.
study.optimize(objective, n_trials=100)
To get the updated number of trials:
len(study.trials)
200
As the objective function is so easy that the last 100 trials don’t improve the result. However, we can check the result again:
best_params = study.best_params
found_x = best_params["x"]
print("Found x: {}, (x - 2)^2: {}".format(found_x, (found_x - 2) ** 2))
Found x: 1.9892141468175906, (x - 2)^2: 0.0001163346288724917
Total running time of the script: ( 0 minutes 0.804 seconds)