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: 1.9907793146555537, (x - 2)^2: 8.502103822128699e-05
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': 1.9907793146555537}
To get the best observed value of the objective function:
study.best_value
8.502103822128699e-05
To get the best trial:
study.best_trial
FrozenTrial(number=90, values=[8.502103822128699e-05], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 849761), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 853089), params={'x': 1.9907793146555537}, 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=[11.492448774107963], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 548520), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 548930), params={'x': 5.390051441218549}, 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=[83.93248703598593], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 549367), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 549669), params={'x': -7.161467515413998}, 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=[140.55382352624113], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 550053), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 550294), params={'x': -9.855539782154212}, 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=[43.540094610620244], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 550664), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 550904), params={'x': 8.598491843642776}, 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=[27.675408921410135], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 551271), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 551509), params={'x': -3.2607422405407904}, 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=[5.698906836357914], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 551913), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 552163), params={'x': 4.38723832835306}, 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=[51.945124037371116], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 552540), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 552803), params={'x': 9.207296583142053}, 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=[10.503130567101097], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 553170), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 553419), params={'x': 5.2408533701945075}, 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=[16.836040500534803], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 553814), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 554064), params={'x': 6.103174441884576}, 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=[6.197922509671413], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 554430), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 554689), params={'x': -0.48956271454876443}, 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=[0.10742445680639973], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 555049), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 558590), params={'x': 1.6722432963211893}, 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=[0.14045301572211683], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 559014), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 562147), params={'x': 1.625229382525635}, 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=[1.8414954349754022], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 562643), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 565724), params={'x': 0.6429828906843501}, 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=[0.5345670965736223], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 566135), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 569203), params={'x': 1.2688590446612757}, 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=[16.330434906309947], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 569635), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 572705), params={'x': -2.041093281070105}, 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=[0.33649413851274357], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 573134), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 576194), params={'x': 2.580081148213544}, 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=[44.37657613123245], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 576623), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 579697), params={'x': -4.661574598488892}, 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=[0.651844902189058], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 580123), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 583176), params={'x': 2.8073691238764695}, 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=[18.570368571310432], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 583614), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 586708), params={'x': -2.3093350497855742}, 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=[57.037801144544986], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 587123), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 590248), params={'x': -5.552337462305626}, 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=[30.860040196452108], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 590660), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 593791), params={'x': 7.555181382857999}, 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=[0.6382270406968001], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 594211), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 597370), params={'x': 2.79889113194277}, 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=[0.6923896396115904], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 597805), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 600913), params={'x': 2.8320995370817066}, 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=[5.820766838971358], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 601328), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 604423), params={'x': -0.4126265436182528}, 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=[0.17761526225255497], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 604865), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 607959), params={'x': 1.5785557424135963}, 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=[0.7459292066589036], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 608393), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 611498), params={'x': 1.1363280676906864}, 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=[4.309310978044483], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 611959), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 615035), params={'x': 4.075887997471078}, 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=[10.010496522201137], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 615452), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 618605), params={'x': -1.1639368707673576}, 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=[26.344844638001614], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 619023), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 622218), params={'x': 7.132722926284022}, 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=[0.0029565018860014764], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 622637), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 625836), params={'x': 1.9456262757758724}, 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=[5.700364012922676], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 626252), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 629542), params={'x': 4.387543510163255}, 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=[0.1005466085073329], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 629961), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 633321), params={'x': 1.6829091478655795}, 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=[4.331311715027064], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 633764), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 636940), params={'x': -0.0811803658085628}, 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=[0.10412876462989268], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 637382), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 640553), params={'x': 1.6773101107411441}, 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=[2.682361273822062], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 640993), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 644152), params={'x': 3.6377915843666013}, 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=[15.311191857257638], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 644584), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 647774), params={'x': 5.912951808706266}, 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=[121.34413816952257], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 648206), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 651353), params={'x': -9.015631537479935}, 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=[28.92573274549941], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 651807), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 654992), params={'x': -3.378264845235814}, 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=[14.348117150319013], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 655412), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 658609), params={'x': -1.7878908577622736}, 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=[2.3639480284251255], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 659026), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 662261), params={'x': 0.4624864135803139}, 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=[8.94333598140593], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 662679), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 665939), params={'x': 4.990541085055668}, 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=[0.0012583787885909962], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 666356), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 669579), params={'x': 2.035473635119494}, 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=[0.0003665548106848909], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 669997), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 673196), params={'x': 1.9808543788117259}, 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=[2.2790408572080936], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 673639), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 676915), params={'x': 3.509649249729252}, 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=[0.0004643247712988845], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 677332), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 680543), params={'x': 2.0215481964743893}, 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=[0.05801156474564025], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 680987), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 684172), params={'x': 2.240855900375391}, 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=[8.14079588974466], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 684606), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 687848), params={'x': -0.853207999733749}, 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=[1.9720371564640053], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 688288), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 691479), params={'x': 0.5957075958106142}, 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=[0.09894691838980137], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 691948), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 695142), params={'x': 2.3145582909252296}, 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=[10.842515185117934], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 695572), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 698816), params={'x': 5.292797471014264}, 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=[24.992322715355414], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 699234), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 702473), params={'x': 6.99923221258579}, 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=[0.09097444662604769], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 702896), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 706124), params={'x': 2.3016197053013077}, 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=[1.7208381117538007], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 706543), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 709831), params={'x': 3.3118071930561293}, 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=[0.008551040450221079], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 710251), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 713458), params={'x': 2.092471835983834}, 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=[1.512771412328841], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 713899), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 717118), params={'x': 0.7700522725217787}, 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=[6.6093698644337655], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 717569), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 721549), params={'x': 4.570869476351097}, 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=[3.8926211458432523], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 721989), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 725856), params={'x': 0.02702733271764446}, 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=[0.14568030507821553], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 726308), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 729767), params={'x': 2.3816808943059837}, 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=[62.802026247420734], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 730192), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 733401), params={'x': 9.9247729461115}, 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=[2.7367713200030632], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 733856), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 737088), params={'x': 3.654318989797029}, 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=[11.122663364865597], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 737529), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 740735), params={'x': -1.3350657212213368}, 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=[0.0024935877528612844], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 741172), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 744418), params={'x': 1.9500641636411156}, 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=[0.5105953722878653], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 744868), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 748064), params={'x': 1.285440434751682}, 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=[0.031095840986234], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 748504), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 751763), params={'x': 2.176340128689513}, 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=[1.2832641421482183], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 752203), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 755443), params={'x': 3.1328124920516274}, 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=[3.3807993511753187], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 755923), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 759172), params={'x': 0.16130498690638784}, 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=[0.009179384877172474], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 759629), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 762889), params={'x': 1.9041908935582192}, 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=[0.7868774697731085], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 763313), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 766606), params={'x': 1.1129388579285482}, 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=[4.790296083515173], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 767032), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 770319), params={'x': 4.188674503784236}, 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=[22.24042038148928], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 770746), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 774038), params={'x': -2.715975019175704}, 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=[0.07613539104474974], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 774466), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 777752), params={'x': 1.7240735767550528}, 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=[1.0519563985170208], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 778179), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 781451), params={'x': 3.0256492570645293}, 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=[0.02238867919582779], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 781900), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 785159), params={'x': 2.149628470538958}, 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=[5.516293372051551], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 785601), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 788896), params={'x': -0.3486790696158448}, 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=[1.2048395114194672], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 789328), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 792625), params={'x': 0.9023481829744611}, 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=[3.45314950173859], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 793073), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 796358), params={'x': 3.8582651860643007}, 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=[0.06836758781134546], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 796813), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 800083), params={'x': 1.7385280362804734}, 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=[0.9721766103266828], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 800529), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 803848), params={'x': 2.985990167459434}, 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=[14.248046933212127], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 804295), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 807581), params={'x': 5.774658518755323}, 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=[7.281625705746473], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 808043), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 811308), params={'x': 4.698448759147832}, 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=[0.0026742698168458865], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 811773), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 815050), params={'x': 1.948286657264823}, 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=[0.0024252937730133897], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 815483), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 818855), params={'x': 1.9507527282683255}, 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=[2.7009517399734397], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 819288), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 822659), params={'x': 0.3565427477499028}, 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=[0.49861396679327175], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 823091), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 826477), params={'x': 1.2938739724431114}, 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=[0.4676643327908487], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 826913), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 830264), params={'x': 2.683859878038512}, 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=[0.03351598031944067], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 830696), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 834065), params={'x': 1.8169262981216563}, 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=[1.2718187306464346], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 834495), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 837941), params={'x': 0.8722505904916489}, 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=[6.828628391828062], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 838373), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 841755), params={'x': -0.6131644402578387}, 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=[1.9014007403428421], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 842187), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 845528), params={'x': 3.3789128835219584}, 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=[0.4868680177901355], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 845961), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 849298), params={'x': 2.697759283557113}, 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=[8.502103822128699e-05], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 849761), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 853089), params={'x': 1.9907793146555537}, 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=[0.03102741770100473], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 853547), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 856883), params={'x': 1.823853987552926}, 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=[0.4617761058561732], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 857322), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 860671), params={'x': 1.3204589005393617}, 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=[2.3233508359752837], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 861126), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 864479), params={'x': 0.4757458099203782}, 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=[0.2809854120201275], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 864941), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 868268), params={'x': 2.530080571253208}, 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=[4.020894077356304], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 868723), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 872063), params={'x': 4.00521671580812}, 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=[0.0011813110940782517], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 872516), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 875881), params={'x': 2.0343702064887346}, 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=[5.038814236290377], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 876335), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 879703), params={'x': -0.24473032596131183}, 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=[1.9603500402199097], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 880159), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 883508), params={'x': 3.400125008783112}, 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=[0.7373223449148858], datetime_start=datetime.datetime(2022, 8, 8, 6, 16, 36, 883993), datetime_complete=datetime.datetime(2022, 8, 8, 6, 16, 36, 887338), params={'x': 1.1413252391534465}, 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: 1.9942968838731217, (x - 2)^2: 3.2525533556659905e-05
Total running time of the script: ( 0 minutes 0.770 seconds)