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: 1.9832077725576471, (x - 2)^2: 0.0002819789024757088
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': 1.9832077725576471}
To get the best observed value of the objective function:
study.best_value
0.0002819789024757088
To get the best trial:
study.best_trial
FrozenTrial(number=84, values=[0.0002819789024757088], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 225026), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 228808), params={'x': 1.9832077725576471}, 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)
To get all trials:
study.trials
[FrozenTrial(number=0, values=[54.337152313900546], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 905363), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 905829), params={'x': 9.371373841686538}, 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=[4.743912079530638], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 906341), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 906660), params={'x': 4.178052359226159}, 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=[0.5649515683669276], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 907126), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 907412), params={'x': 2.751632601985124}, 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=[105.33599690515982], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 907820), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 908118), params={'x': -8.263332641260334}, 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=[36.45760902510809], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 908514), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 908795), params={'x': 8.038013665528432}, 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=[38.709783985094845], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 909139), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 909390), params={'x': -4.221718732399822}, 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=[122.95676395600447], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 909774), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 910034), params={'x': -9.088587103684782}, 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=[0.6596409173201925], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 910413), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 910681), params={'x': 2.812182810283616}, 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=[41.84541169605032], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 911271), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 911568), params={'x': -4.468802956965865}, 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=[41.76623457315913], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 911985), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 912282), params={'x': 8.462680138546169}, 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=[7.30696877786048], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 912658), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 916567), params={'x': -0.7031405397907968}, 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=[1.2414369528465805], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 917133), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 920525), params={'x': 3.114197896626349}, 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=[1.2312874988806817], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 921099), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 924479), params={'x': 3.1096339481471724}, 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=[5.648967576422743], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 925061), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 928456), params={'x': -0.37675568294739614}, 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=[7.468498914643857], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 929040), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 932447), params={'x': 4.7328554507408285}, 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=[0.6024510149708567], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 933031), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 936442), params={'x': 1.223822819859501}, 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=[26.643115172324546], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 937031), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 940406), params={'x': -3.1616969275931477}, 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=[18.827604248476366], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 941006), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 944419), params={'x': 6.339078732689275}, 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=[1.5937767698641072], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 945003), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 948409), params={'x': 0.7375512803031928}, 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=[0.8137180148370787], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 948997), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 952434), params={'x': 1.097936801084825}, 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=[19.01180582555947], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 953016), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 956424), params={'x': -2.3602529543088977}, 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=[14.53132949177832], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 957008), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 960643), params={'x': 5.811998097032358}, 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=[0.05853866036748421], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 961236), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 964660), params={'x': 2.241947639722904}, 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=[0.26944922156605744], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 965245), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 968699), params={'x': 1.4809150150832164}, 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=[15.066644500528954], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 969284), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 972733), params={'x': -1.8815775788368514}, 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=[0.044078162130795025], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 973319), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 976783), params={'x': 2.2099479986348882}, 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=[56.04948918679602], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 977369), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 980802), params={'x': -5.486620678703845}, 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=[23.171269213719803], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 981389), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 984838), params={'x': 6.813654455163956}, 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=[0.025061645030227224], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 985436), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 988949), params={'x': 1.841691298311725}, 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=[8.370292029407073], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 989536), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 993045), params={'x': 4.8931456979224315}, 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=[62.59975657771797], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 993639), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 3, 997148), params={'x': 9.912000794850691}, 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=[0.028545483188776876], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 3, 997739), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 1299), params={'x': 1.8310459139624706}, 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=[6.5364120974459645], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 1903), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 5480), params={'x': -0.5566407838110472}, 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=[0.0161531050455548], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 6093), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 9620), params={'x': 2.1270948663225813}, 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=[5.2152969574825745], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 10210), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 13758), params={'x': 4.283702466934468}, 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=[3.027680405771287], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 14345), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 17866), params={'x': 0.2599768950467103}, 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=[2.7731831123478754], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 18456), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 22011), params={'x': 3.6652876965701378}, 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=[13.202283894936377], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 22600), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 26140), params={'x': -1.633494722018511}, 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=[0.015643734032872347], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 26730), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 30265), params={'x': 2.1250749136832496}, 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=[12.234178212010601], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 30900), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 34391), params={'x': 5.497739014279167}, 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=[72.06326003954594], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 35041), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 38574), params={'x': -6.48900818939091}, 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=[0.001639417993731076], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 39191), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 42707), params={'x': 2.040489727014776}, 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=[0.011681844834906167], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 43324), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 46874), params={'x': 2.1080825834022585}, 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=[2.9752656164820284], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 47467), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 51031), params={'x': 3.724895827718888}, 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=[2.2811558610620364], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 51622), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 55195), params={'x': 0.48965041759795347}, 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=[0.4163177529448839], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 55806), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 59359), params={'x': 2.645226900357451}, 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=[9.394664469295254], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 59958), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 63595), params={'x': -1.065071690726867}, 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=[2.2247749691989163], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 64213), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 67796), params={'x': 3.49156795661442}, 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=[3.688454802392281], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 68405), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 72379), params={'x': 0.07946496975653128}, 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=[25.86072783472476], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 72982), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 76623), params={'x': 7.085344416529205}, 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=[0.021074903344405482], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 77221), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 80869), params={'x': 1.8548280214903528}, 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=[0.0028384145369908225], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 81474), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 85103), params={'x': 2.0532767729596193}, 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=[0.6429513198520862], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 85718), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 89371), params={'x': 2.8018424532612913}, 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=[5.193767313715957], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 89966), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 93614), params={'x': 4.278983833579334}, 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=[0.2529255300328374], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 94204), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 97796), params={'x': 1.4970829789788007}, 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=[1.5834337101908744], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 98392), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 102268), params={'x': 0.7416543757016221}, 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=[0.5329181424867424], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 102895), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 106567), params={'x': 2.730012426255021}, 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=[8.335805733019296], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 107191), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 110777), params={'x': -0.8871795463772767}, 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=[8.703703548258186], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 111418), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 115077), params={'x': 4.950203984177736}, 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=[0.4667509884136149], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 115697), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 119326), params={'x': 1.3168082345244383}, 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=[4.404356740098728], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 119930), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 123610), params={'x': -0.09865593656957675}, 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=[0.027096207929901864], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 124226), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 127869), params={'x': 2.1646092583359207}, 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=[0.010843566422919263], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 128490), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 132165), params={'x': 2.1041324465424647}, 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=[1.2779787652347976], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 132764), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 136841), params={'x': 3.130477228976682}, 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=[3.6782085288701833], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 137567), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 141577), params={'x': 3.9178656180426676}, 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=[1.237348012372093], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 142185), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 145864), params={'x': 0.8876385423918658}, 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=[138.01033999001106], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 146472), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 150451), params={'x': -9.747780215428405}, 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=[0.021936740303263993], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 151085), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 154724), params={'x': 2.1481105678311443}, 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=[1.7451573726740792], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 155379), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 159224), params={'x': 3.321044046454954}, 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=[26.67262748651931], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 159839), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 163518), params={'x': -3.1645549165943927}, 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=[0.12101844988545599], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 164145), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 167845), params={'x': 1.6521229385465952}, 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=[0.11652661923935913], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 168478), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 172196), params={'x': 2.3413599555298763}, 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=[0.013347440902435299], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 172805), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 176494), params={'x': 2.115531125253913}, 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=[1.1584043097922816], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 177108), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 180819), params={'x': 0.9237080740838564}, 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=[0.9648519579330496], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 181431), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 185167), params={'x': 2.982268780901159}, 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=[0.03477339228399483], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 185787), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 189558), params={'x': 1.8135237487399674}, 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=[5.379884712481897], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 190182), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 193912), params={'x': 4.319457848826294}, 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=[2.9415948752847854], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 194524), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 198244), params={'x': 0.28489216803001405}, 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=[10.084979602185113], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 198881), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 202573), params={'x': 5.1756856900809805}, 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=[0.5138857864496027], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 203210), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 206930), params={'x': 1.2831417249904953}, 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=[0.26128268216805606], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 207536), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 211282), params={'x': 2.511158177248546}, 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=[0.014768950314844629], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 211903), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 215660), params={'x': 2.1215275701840723}, 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=[1.7832108663984698], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 216283), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 220039), params={'x': 3.335369187303073}, 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=[5.331295574367087], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 220671), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 224417), params={'x': -0.3089598468503274}, 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=[0.0002819789024757088], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 225026), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 228808), params={'x': 1.9832077725576471}, 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=[1.0465656840365356], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 229411), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 233185), params={'x': 0.9769820705204939}, 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=[3.9207458197647114], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 233793), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 237599), params={'x': 3.980087326297684}, 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=[0.2559671733161117], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 238209), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 241995), params={'x': 2.505931984871595}, 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=[11.285789228539715], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 242613), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 246395), params={'x': -1.3594328730515979}, 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=[2.1350997438839987], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 247111), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 250883), params={'x': 0.5388019491239393}, 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=[0.046586896651925384], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 251496), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 255352), params={'x': 1.7841600207284911}, 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=[0.0008964734911618967], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 255968), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 259771), params={'x': 2.0299411671643224}, 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=[0.6060570873862782], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 260404), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 264184), params={'x': 1.2215033157512627}, 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=[6.516910323748762], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 264798), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 268582), params={'x': 4.552823989966555}, 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=[0.5581516673569155], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 269197), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 273008), params={'x': 2.747095487442479}, 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=[2.677013058188546], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 273628), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 277403), params={'x': 3.6361580174874755}, 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=[0.0026709920695410314], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 278018), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 281827), params={'x': 2.0516816415136074}, 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=[1.4470491596508066], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 282447), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 286233), params={'x': 3.2029335641051864}, 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=[0.15952366183417704], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 286883), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 290681), params={'x': 1.6005958665284283}, 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=[0.018922640655417593], datetime_start=datetime.datetime(2022, 12, 1, 6, 17, 4, 291328), datetime_complete=datetime.datetime(2022, 12, 1, 6, 17, 4, 295522), params={'x': 2.1375595894709547}, 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: 2.0010547551772095, (x - 2)^2: 1.1125084838503348e-06
Total running time of the script: ( 0 minutes 0.894 seconds)