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))
Out:
Found x: 1.9979710368220647, (x - 2)^2: 4.116691577417425e-06
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
Out:
{'x': 1.9979710368220647}
To get the best observed value of the objective function:
study.best_value
Out:
4.116691577417425e-06
To get the best trial:
study.best_trial
Out:
FrozenTrial(number=58, values=[4.116691577417425e-06], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 619996), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 623428), params={'x': 1.9979710368220647}, 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)
To get all trials:
study.trials
Out:
[FrozenTrial(number=0, values=[92.10359368229653], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 419700), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 420120), params={'x': -7.597061721292436}, 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=[13.823698444496161], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 420592), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 420877), params={'x': 5.718023459379481}, 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=[20.48416079750555], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 421307), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 421576), params={'x': -2.525943083767796}, 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=[27.25410582086926], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 421992), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 422276), params={'x': 7.220546505957902}, 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=[1.7414612919926118], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 422691), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 422942), params={'x': 3.3196443808816873}, 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=[43.74774047878632], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 423324), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 423566), params={'x': 8.614207471707122}, 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=[45.27449865119015], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 423991), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 424262), params={'x': 8.728632747534238}, 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=[31.082459709921718], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 424681), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 424960), params={'x': 7.5751645455467695}, 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=[141.00034415050044], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 425380), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 425656), params={'x': -9.874356578379329}, 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=[21.77932716983913], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 426059), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 426326), params={'x': -2.666832670006407}, 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=[0.30327721069614394], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 426686), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 430480), params={'x': 2.5507061019238337}, 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=[0.4658570594345077], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 431004), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 434536), params={'x': 2.682537222013941}, 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=[0.0021453015574535842], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 435001), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 438374), params={'x': 1.9536825998413816}, 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=[1.593257228232636], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 438839), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 442343), params={'x': 0.7377570644948588}, 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=[15.14912316754324], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 442809), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 446163), params={'x': -1.8921874527755262}, 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=[0.006314312771896738], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 446630), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 449954), params={'x': 2.0794626501691}, 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=[46.84969085469566], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 450415), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 454066), params={'x': -4.844683400618005}, 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=[5.9167735374363035], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 454554), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 458036), params={'x': 4.432441887781968}, 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=[3.60789973940418], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 458500), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 461918), params={'x': 0.10055278056899408}, 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=[0.7116594646803288], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 462380), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 465829), params={'x': 1.1564008862733859}, 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=[10.492690360365868], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 466298), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 469773), params={'x': 5.239242250954051}, 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=[0.008924504737964606], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 470242), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 473867), params={'x': 1.905530403102561}, 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=[7.195299253450807], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 474340), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 477735), params={'x': -0.6824054975806337}, 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=[0.004737823927599563], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 478202), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 481760), params={'x': 2.068831852565506}, 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=[4.022072540172414], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 482261), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 485585), params={'x': 4.00551054352063}, 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=[35.770105127337914], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 486053), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 489782), params={'x': -3.9808114104474077}, 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=[7.911283873453341], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 490380), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 494216), params={'x': -0.8127004592478988}, 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=[17.511414748053365], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 494718), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 498046), params={'x': 6.1846642336098325}, 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=[0.19297051940098967], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 498511), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 501921), params={'x': 1.5607159012654912}, 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=[62.941059092334065], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 502389), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 505804), params={'x': -5.93354013617717}, 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=[4.542957339047146], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 506275), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 509735), params={'x': 4.131421436283108}, 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=[0.029652835767779162], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 510236), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 513670), params={'x': 1.8278000122886788}, 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=[3.670220574524012], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 514170), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 518413), params={'x': 0.08421802531602984}, 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=[0.08784896671987248], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 518922), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 522327), params={'x': 2.2963932636209408}, 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=[16.426810740063114], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 522801), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 526264), params={'x': 6.053000214663591}, 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=[11.975185019665158], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 526735), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 530195), params={'x': -1.4605180276463172}, 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=[1.5558365194351338], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 530698), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 534203), params={'x': 3.247331759972115}, 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=[9.014413858586348], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 534708), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 538144), params={'x': 5.00240134868514}, 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=[1.3986418770968667], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 538649), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 542322), params={'x': 0.8173580943088197}, 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=[26.238026908582803], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 542794), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 546258), params={'x': 7.1223067956324915}, 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=[22.587506976400427], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 546730), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 550224), params={'x': -2.752631584333087}, 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=[0.059953011109025546], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 550701), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 554219), params={'x': 1.7551469601801408}, 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=[1.6267577024959892], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 554741), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 558163), params={'x': 3.2754441197073234}, 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=[0.050218610659566267], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 558642), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 562114), params={'x': 2.224095092894883}, 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=[5.182153754667049], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 562629), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 566349), params={'x': -0.2764344389125397}, 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=[2.0299888242306197], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 566900), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 570900), params={'x': 3.424776762945908}, 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=[0.001404734834478404], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 571434), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 574989), params={'x': 1.9625202076516104}, 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=[2.157286896482805], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 575529), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 578942), params={'x': 0.5312294609154209}, 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=[132.52480314492524], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 579481), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 582956), params={'x': -9.511941762575297}, 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=[0.9674520427539856], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 583450), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 587024), params={'x': 2.9835914003050177}, 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=[11.542445685041345], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 587556), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 591032), params={'x': -1.3974175023157438}, 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=[0.16179668119184468], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 591558), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 595000), params={'x': 1.5977604181686682}, 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=[0.20927662424209964], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 595600), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 599006), params={'x': 2.4574676209767197}, 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=[1.4407659460540747], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 599501), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 603140), params={'x': 0.7996808982382748}, 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=[4.0262955414454344], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 603647), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 607150), params={'x': 4.006563116736036}, 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=[9.199615425641733], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 607683), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 611106), params={'x': 5.033086781752499}, 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=[0.16973194028783], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 611654), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 615376), params={'x': 1.5880146358329825}, 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=[6.594442859702449], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 615899), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 619464), params={'x': -0.567964731008284}, 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=[4.116691577417425e-06], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 619996), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 623428), params={'x': 1.9979710368220647}, 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=[3.0685634696242294], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 623964), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 627361), params={'x': 0.2482684367677137}, 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=[7.047335071095758], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 627869), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 631535), params={'x': 4.654681726892276}, 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=[0.012553960793001398], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 632063), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 635624), params={'x': 2.1120444590017793}, 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=[3.2062934164142276], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 636155), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 639917), params={'x': 3.790612581329146}, 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=[0.19898522011697475], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 640434), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 643909), params={'x': 2.446077594278142}, 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=[0.7986749822112298], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 644387), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 647878), params={'x': 1.106313823419412}, 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=[0.660735145566411], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 648405), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 651891), params={'x': 2.8128561653616284}, 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=[0.8585772834842568], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 652430), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 656252), params={'x': 1.0734055452981295}, 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=[13.098040784538728], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 656770), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 660243), params={'x': 5.61912154873786}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=67, state=TrialState.COMPLETE, value=None), FrozenTrial(number=68, values=[0.009634127370253131], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 660774), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 664258), params={'x': 2.0981535907150275}, 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=[2.8262263696416454], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 664772), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 668426), params={'x': 3.6811384147778092}, 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=[58.525527936724835], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 668951), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 672639), params={'x': 9.650197901801288}, 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=[0.0037575641461844453], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 673113), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 676658), params={'x': 1.9387010265486897}, 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=[0.7722395982882204], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 677127), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 680680), params={'x': 2.8787716417182683}, 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=[3.4055053482152777], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 681154), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 684888), params={'x': 0.15459886522867938}, 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=[0.19355147424289706], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 685369), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 688912), params={'x': 1.5600551463616184}, 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=[6.496974344886899], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 689445), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 692985), params={'x': 4.548916307940867}, 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=[0.49200287426163125], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 693466), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 697279), params={'x': 1.2985708344660658}, 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=[8.602495090255099], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 697785), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 701358), params={'x': -0.9330010382294616}, 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=[8.38487640335236e-06], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 701834), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 705533), params={'x': 2.0028956651055245}, 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=[1.6386666467872597], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 706056), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 710376), params={'x': 3.2801041546636975}, 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=[1.992008961243642], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 710854), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 714381), params={'x': 0.5886145242196794}, 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=[0.0033203956804747727], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 714879), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 718856), params={'x': 2.057622874628699}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=81, state=TrialState.COMPLETE, value=None), FrozenTrial(number=82, values=[0.5689715627173974], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 719359), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 723264), params={'x': 2.754302036797858}, 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=[0.0017114985383479269], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 723819), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 727567), params={'x': 1.9586297384786133}, 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=[5.24894966216996], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 728080), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 731819), params={'x': -0.2910586335076544}, 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=[0.009122454759600654], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 732267), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 736208), params={'x': 2.0955115425464412}, 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=[0.6221202177473509], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 736718), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 740720), params={'x': 1.2112540220404602}, 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=[1.8191504137255916], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 741249), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 745571), params={'x': 0.651241158054713}, 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=[4.778160839641958], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 746054), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 749850), params={'x': 4.185900464257684}, 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=[0.3432850984088243], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 750353), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 754272), params={'x': 2.58590536642774}, 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=[1.9814664602889065], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 754789), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 758896), params={'x': 3.4076457154727913}, 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=[0.025043421837664982], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 759418), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 763131), params={'x': 1.841748864656}, 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=[1.0004794127061813], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 763783), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 767510), params={'x': 3.0002396776304074}, 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=[0.03158803362529488], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 768060), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 772035), params={'x': 1.8222697728992199}, 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=[0.33296920123899487], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 772588), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 776334), params={'x': 1.4229651646226245}, 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=[0.14035815666548368], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 776835), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 780983), params={'x': 2.374644039943896}, 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=[2.8648982114496415], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 781525), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 785739), params={'x': 0.30739898042992975}, 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=[0.9774782050800246], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 786258), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 790231), params={'x': 1.0113250255619775}, 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=[2.905778800025638], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 790792), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 794645), params={'x': 3.7046345062873853}, 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=[0.005493912588001782], datetime_start=datetime.datetime(2022, 6, 6, 7, 10, 59, 795157), datetime_complete=datetime.datetime(2022, 6, 6, 7, 10, 59, 799337), params={'x': 1.9258790678148083}, 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)
Out:
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)
Out:
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))
Out:
Found x: 1.9979710368220647, (x - 2)^2: 4.116691577417425e-06
Total running time of the script: ( 0 minutes 0.857 seconds)