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: 1.9966964963253655, (x - 2)^2: 1.0913136528323647e-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': 1.9966964963253655}
To get the best observed value of the objective function:
study.best_value
1.0913136528323647e-05
To get the best trial:
study.best_trial
FrozenTrial(number=92, values=[1.0913136528323647e-05], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 152712), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 155971), params={'x': 1.9966964963253655}, 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)
To get all trials:
study.trials
[FrozenTrial(number=0, values=[8.758202459469405], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 629662), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 630439), params={'x': -0.9594260354787387}, 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=[56.662016617782754], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 631500), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 631895), params={'x': 9.527417659316026}, 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=[11.36951773463181], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 632875), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 633153), params={'x': -1.3718715477656929}, 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=[10.486594086900604], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 634062), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 634406), params={'x': 5.238301111215664}, 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=[14.045328106090164], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 635277), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 635650), params={'x': -1.747709714757823}, 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=[106.6367527513734], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 636499), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 636906), params={'x': -8.326507287140865}, 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=[3.7062545012024035], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 637721), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 638138), params={'x': 3.925163499862389}, 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=[67.67184743215323], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 638973), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 639339), params={'x': -6.226290016292473}, 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=[2.131899231997651], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 640182), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 640567), params={'x': 0.5398975268846193}, 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=[41.3726762363871], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 641388), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 641752), params={'x': -4.432159531322828}, 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=[1.9774576732199944], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 642623), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 649618), params={'x': 3.4062210612915718}, 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=[4.314567060001015], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 650635), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 656525), params={'x': 4.0771535956690865}, 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=[0.0681177028537647], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 657691), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 663935), params={'x': 2.2609936835514697}, 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=[30.27150304464783], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 664951), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 671146), params={'x': 7.501954474970493}, 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=[0.47041001655194353], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 672101), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 677864), params={'x': 1.3141355698449266}, 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=[0.013067542584701925], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 678936), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 684816), params={'x': 2.1143133526089666}, 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=[26.096859111655725], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 685892), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 691950), params={'x': 7.108508501672061}, 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=[36.56873136472156], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 693072), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 699672), params={'x': -4.047208559717579}, 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=[0.054047570765593085], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 700793), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 706963), params={'x': 2.232481334230499}, 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=[25.228445653763604], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 708006), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 713896), params={'x': -3.0227926150462956}, 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=[13.879012522646796], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 714862), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 720683), params={'x': 5.725454673277719}, 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=[0.44928401407609053], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 721793), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 727694), params={'x': 1.329713483593702}, 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=[0.1779067678699691], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 728803), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 734913), params={'x': 2.4217899570520487}, 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=[0.06780182303279204], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 735896), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 742086), params={'x': 2.2603878319599287}, 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=[5.09357368680023], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 743170), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 749588), params={'x': -0.2568946999805351}, 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=[15.170049963650616], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 750635), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 757107), params={'x': 5.894874832860565}, 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=[0.023107251806386987], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 758134), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 764116), params={'x': 1.8479893036448192}, 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=[3.379272727972485], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 765064), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 771178), params={'x': 0.16172017147212192}, 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=[18.750679974307427], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 772181), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 778475), params={'x': -2.330205534880235}, 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=[51.57293875338196], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 779450), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 785803), params={'x': 9.181430132876178}, 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=[5.688670004998041], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 786707), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 793562), params={'x': 4.385093290627862}, 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=[0.818462732507256], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 794722), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 801211), params={'x': 2.9046893016429762}, 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=[0.6829302958445208], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 802193), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 808310), params={'x': 1.1736040320496954}, 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=[6.583602024148237], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 809361), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 815494), params={'x': -0.5658530792210681}, 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=[0.5461432077629116], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 816680), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 823112), params={'x': 2.739015025397259}, 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=[0.0199424123209145], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 824121), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 830578), params={'x': 2.1412176062710118}, 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=[8.307110947365091], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 831620), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 837900), params={'x': 4.882205916891625}, 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=[9.253581804635216], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 839027), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 845706), params={'x': -1.0419700532114406}, 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=[20.894334745618966], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 846707), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 852955), params={'x': 6.571032131326465}, 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=[42.48901071034571], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 854072), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 860373), params={'x': 8.518359510670281}, 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=[0.8523661756731515], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 861510), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 867853), params={'x': 1.0767632071493514}, 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=[0.012897819176376652], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 869070), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 876207), params={'x': 2.113568565969535}, 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=[2.809186880372417], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 877256), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 883684), params={'x': 3.6760629106249016}, 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=[0.013249511522982874], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 884566), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 890696), params={'x': 1.8848934774959174}, 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=[116.75335648053228], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 891651), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 897876), params={'x': -8.805246710766593}, 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=[2.306177659611023], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 898709), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 904608), params={'x': 0.4813895629191063}, 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=[16.155658983846696], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 905553), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 912600), params={'x': -2.019410278118756}, 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=[7.553868552771481], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 913570), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 919689), params={'x': 4.748430197907795}, 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=[8.414211770531091], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 920669), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 926743), params={'x': -0.9007260764386376}, 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=[1.8360382356842728], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 927628), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 933783), params={'x': 3.355004884007535}, 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=[0.2666231200787737], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 934837), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 941489), params={'x': 1.4836443860295758}, 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=[0.0728075072339672], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 942469), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 948615), params={'x': 2.269828662736128}, 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=[0.037336342782628505], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 949675), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 956789), params={'x': 1.8067738558511595}, 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=[2.1213362332620713], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 957824), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 964042), params={'x': 0.543519230040413}, 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=[2.474294901799742], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 965173), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 971549), params={'x': 3.5729891613738927}, 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=[0.024483666816348698], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 972505), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 978742), params={'x': 1.8435274247149083}, 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=[141.3808228071466], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 979800), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 985942), params={'x': -9.890366807089956}, 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=[1.2213146186950201], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 987086), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 35, 994101), params={'x': 3.1051310414131983}, 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=[4.1355662265546815], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 35, 995116), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 1906), params={'x': -0.033609162684580696}, 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=[4.042972902901123], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 3020), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 9400), params={'x': 4.0107145254613155}, 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=[12.398567610420471], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 10527), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 17664), params={'x': 5.521159980804688}, 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=[0.15704864527495332], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 18768), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 24878), params={'x': 1.6037063648316399}, 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=[0.0004256824856603371], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 26023), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 32918), params={'x': 1.9793679258032466}, 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=[1.8554207353298695], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 33972), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 41050), params={'x': 0.6378617047708153}, 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=[0.005814984107377845], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 42284), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 46521), params={'x': 1.9237439569124004}, 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=[0.712674351150606], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 47087), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 50349), params={'x': 2.8442004211978373}, 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=[13.042097821552957], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 50876), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 54114), params={'x': -1.6113844743467785}, 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=[0.7622091460806163], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 54634), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 57878), params={'x': 1.1269540985259616}, 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=[5.45212354814825], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 58395), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 61794), params={'x': 4.334978275733684}, 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=[0.1632999831672067], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 62311), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 65551), params={'x': 2.4041039261962283}, 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=[5.813553912054834], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 66083), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 69327), params={'x': -0.411131251519675}, 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=[0.0031456130982241543], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 69857), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 73093), params={'x': 1.9439142344420248}, 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=[0.0015878996747351018], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 73618), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 76858), params={'x': 2.0398484588752828}, 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=[1.3157803529625995], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 77378), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 80634), params={'x': 0.8529253062844602}, 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=[0.6655786941331246], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 81156), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 85192), params={'x': 2.815830064494515}, 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=[3.6214548827819906], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 85716), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 88954), params={'x': 0.09698794465668437}, 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=[0.0002316626356266225], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 89481), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 93118), params={'x': 2.0152204676546623}, 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=[2.4119194183902466], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 93693), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 98353), params={'x': 3.5530355496221735}, 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=[0.07325088378102458], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 99020), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 102318), params={'x': 1.7293509952336337}, 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=[0.3889283535464518], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 102854), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 106137), params={'x': 2.623641205779775}, 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=[9.43929480554296], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 106661), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 109940), params={'x': 5.072343536381139}, 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=[0.0031679147151751946], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 110468), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 113804), params={'x': 2.0562842314967096}, 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=[1.4771147335360049], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 114330), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 117595), params={'x': 3.2153660903349266}, 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=[0.7019795431968044], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 118136), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 121412), params={'x': 1.162157805313671}, 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=[0.030132947864469056], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 121948), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 125212), params={'x': 2.1735884439254787}, 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=[5.079725787121888], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 125745), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 129016), params={'x': 4.253824701950418}, 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=[2.212451986910683], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 129540), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 132849), params={'x': 0.5125686614466256}, 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=[0.3802623196407314], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 133379), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 136688), params={'x': 1.3833458670853398}, 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=[8.961914227867231], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 137213), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 140513), params={'x': -0.9936456416662331}, 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=[3.3887890818266793], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 141050), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 144320), params={'x': 3.8408663943444346}, 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=[0.00011685271221787159], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 144881), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 148321), params={'x': 2.0108098433021886}, 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=[61.20625399664431], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 148883), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 152146), params={'x': -5.82344259240421}, 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=[1.0913136528323647e-05], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 152712), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 155971), params={'x': 1.9966964963253655}, 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=[0.29514003497368274], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 156494), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 159806), params={'x': 2.54326792190749}, 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=[0.003154595828250043], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 160335), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 163650), params={'x': 2.056165788770835}, 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=[1.0617675424561346], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 164178), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 167496), params={'x': 3.030421051054439}, 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=[1.2997849675960231], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 168027), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 171357), params={'x': 0.859918876747789}, 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=[2.902072734656277], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 171890), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 175298), params={'x': 0.2964528962613693}, 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=[0.3154103169362582], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 175828), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 179401), params={'x': 1.43838597156387}, 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=[0.004726392099132953], datetime_start=datetime.datetime(2022, 8, 29, 5, 14, 36, 179936), datetime_complete=datetime.datetime(2022, 8, 29, 5, 14, 36, 183265), params={'x': 2.068748760709797}, 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: 1.9966964963253655, (x - 2)^2: 1.0913136528323647e-05
Total running time of the script: ( 0 minutes 1.002 seconds)