Note
Click here to download the full example code
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: 2.001848144234501, (x - 2)^2: 3.4156371115195874e-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': 2.001848144234501}
To get the best observed value of the objective function:
study.best_value
Out:
3.4156371115195874e-06
To get the best trial:
study.best_trial
Out:
FrozenTrial(number=90, values=[3.4156371115195874e-06], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 601740), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 605093), params={'x': 2.001848144234501}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=90, state=TrialState.COMPLETE, value=None)
To get all trials:
study.trials
Out:
[FrozenTrial(number=0, values=[136.56381038345373], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 299034), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 299449), params={'x': -9.686051958786326}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=0, state=TrialState.COMPLETE, value=None), FrozenTrial(number=1, values=[36.50552462022296], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 299923), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 300190), params={'x': 8.041980190320302}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=1, state=TrialState.COMPLETE, value=None), FrozenTrial(number=2, values=[1.653422071480193], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 300600), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 300854), params={'x': 3.285854607442145}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=2, state=TrialState.COMPLETE, value=None), FrozenTrial(number=3, values=[19.15624670185348], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 301211), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 301451), params={'x': 6.3767849732256074}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=3, state=TrialState.COMPLETE, value=None), FrozenTrial(number=4, values=[31.923246114017367], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 301861), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 302119), params={'x': -3.6500660274033407}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=4, state=TrialState.COMPLETE, value=None), FrozenTrial(number=5, values=[2.5795335884726622], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 302494), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 302747), params={'x': 0.39390735370817964}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=5, state=TrialState.COMPLETE, value=None), FrozenTrial(number=6, values=[6.247003392741436], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 303151), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 303415), params={'x': -0.49940060669382014}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=6, state=TrialState.COMPLETE, value=None), FrozenTrial(number=7, values=[48.76953114081939], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 303767), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 304019), params={'x': -4.983518535868534}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=7, state=TrialState.COMPLETE, value=None), FrozenTrial(number=8, values=[0.10958434659086855], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 304413), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 304680), params={'x': 1.6689647351249892}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=8, state=TrialState.COMPLETE, value=None), FrozenTrial(number=9, values=[141.52161601860448], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 305035), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 305293), params={'x': -9.896285807705045}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=9, state=TrialState.COMPLETE, value=None), FrozenTrial(number=10, values=[1.377329330027827], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 305690), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 309129), params={'x': 3.1735967493256902}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=10, state=TrialState.COMPLETE, value=None), FrozenTrial(number=11, values=[2.320364863388938], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 309584), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 312796), params={'x': 3.523274388739251}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=11, state=TrialState.COMPLETE, value=None), FrozenTrial(number=12, values=[2.0306799417918127], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 313250), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 316470), params={'x': 3.4250192776912924}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=12, state=TrialState.COMPLETE, value=None), FrozenTrial(number=13, values=[4.803371394506356], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 316925), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 320009), params={'x': -0.19165950697327894}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=13, state=TrialState.COMPLETE, value=None), FrozenTrial(number=14, values=[63.299922191317194], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 320466), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 323528), params={'x': 9.956124822507324}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=14, state=TrialState.COMPLETE, value=None), FrozenTrial(number=15, values=[12.522188087521204], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 323985), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 327032), params={'x': 5.538670384130345}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=15, state=TrialState.COMPLETE, value=None), FrozenTrial(number=16, values=[29.25978181059469], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 327488), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 330567), params={'x': -3.409231166311409}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=16, state=TrialState.COMPLETE, value=None), FrozenTrial(number=17, values=[0.04407985867840528], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 331033), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 334038), params={'x': 1.790047961004411}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=17, state=TrialState.COMPLETE, value=None), FrozenTrial(number=18, values=[0.7249341449927926], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 334515), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 337561), params={'x': 1.1485693539736823}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=18, state=TrialState.COMPLETE, value=None), FrozenTrial(number=19, values=[17.067436446057272], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 338017), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 341087), params={'x': -2.1312754018652966}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=19, state=TrialState.COMPLETE, value=None), FrozenTrial(number=20, values=[85.39059288266637], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 341542), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 344645), params={'x': -7.240703051319546}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=20, state=TrialState.COMPLETE, value=None), FrozenTrial(number=21, values=[0.12426595142880097], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 345102), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 348185), params={'x': 1.647486239376672}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=21, state=TrialState.COMPLETE, value=None), FrozenTrial(number=22, values=[0.02552231790832767], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 348641), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 351739), params={'x': 1.8402429409749677}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=22, state=TrialState.COMPLETE, value=None), FrozenTrial(number=23, values=[9.219177863276135], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 352196), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 355276), params={'x': 5.036309908964521}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=23, state=TrialState.COMPLETE, value=None), FrozenTrial(number=24, values=[13.430672994801123], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 355737), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 358837), params={'x': -1.6647882605685589}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=24, state=TrialState.COMPLETE, value=None), FrozenTrial(number=25, values=[0.036750979345556885], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 359315), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 362443), params={'x': 2.1917054494414723}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=25, state=TrialState.COMPLETE, value=None), FrozenTrial(number=26, values=[28.889672854033357], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 362910), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 365956), params={'x': 7.374911427552398}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=26, state=TrialState.COMPLETE, value=None), FrozenTrial(number=27, values=[8.579380257180977], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 366437), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 369482), params={'x': 4.92905791291005}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=27, state=TrialState.COMPLETE, value=None), FrozenTrial(number=28, values=[12.246409114386754], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 369958), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 373105), params={'x': -1.4994869787422773}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=28, state=TrialState.COMPLETE, value=None), FrozenTrial(number=29, values=[0.049684200834272], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 373565), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 376716), params={'x': 1.7771004691923467}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=29, state=TrialState.COMPLETE, value=None), FrozenTrial(number=30, values=[81.02775672228515], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 377178), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 380322), params={'x': -7.001541908044707}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=30, state=TrialState.COMPLETE, value=None), FrozenTrial(number=31, values=[0.0015963783571758116], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 380785), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 383959), params={'x': 2.0399547038178962}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=31, state=TrialState.COMPLETE, value=None), FrozenTrial(number=32, values=[0.5773635590272774], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 384425), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 387593), params={'x': 2.759844430806252}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=32, state=TrialState.COMPLETE, value=None), FrozenTrial(number=33, values=[5.72892693013415], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 388058), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 391218), params={'x': 4.39351768953859}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=33, state=TrialState.COMPLETE, value=None), FrozenTrial(number=34, values=[2.847313200324657], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 391685), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 394835), params={'x': 0.31260164740964114}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=34, state=TrialState.COMPLETE, value=None), FrozenTrial(number=35, values=[0.15100189625903532], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 395302), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 398449), params={'x': 2.3885896244871128}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=35, state=TrialState.COMPLETE, value=None), FrozenTrial(number=36, values=[21.309483847635622], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 398925), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 402050), params={'x': 6.616219648980714}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=36, state=TrialState.COMPLETE, value=None), FrozenTrial(number=37, values=[8.565415012697578], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 402537), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 405687), params={'x': -0.9266730279786257}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=37, state=TrialState.COMPLETE, value=None), FrozenTrial(number=38, values=[1.2835523283233556], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 406151), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 409296), params={'x': 0.8670603156728265}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=38, state=TrialState.COMPLETE, value=None), FrozenTrial(number=39, values=[4.126757284449043], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 409763), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 413272), params={'x': 4.031442168620373}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=39, state=TrialState.COMPLETE, value=None), FrozenTrial(number=40, values=[21.331783254303698], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 413743), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 417100), params={'x': -2.6186343494916007}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=40, state=TrialState.COMPLETE, value=None), FrozenTrial(number=41, values=[0.01887197166885844], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 417569), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 420744), params={'x': 2.1373752949727804}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=41, state=TrialState.COMPLETE, value=None), FrozenTrial(number=42, values=[0.08378579588708061], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 421214), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 424408), params={'x': 2.2894577618359553}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=42, state=TrialState.COMPLETE, value=None), FrozenTrial(number=43, values=[2.3089540120225647], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 424876), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 428348), params={'x': 0.4804757283864911}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=43, state=TrialState.COMPLETE, value=None), FrozenTrial(number=44, values=[0.45674622255572805], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 428819), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 432443), params={'x': 2.6758300248995512}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=44, state=TrialState.COMPLETE, value=None), FrozenTrial(number=45, values=[3.7487357344039323], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 432912), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 436104), params={'x': 3.936165213612705}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=45, state=TrialState.COMPLETE, value=None), FrozenTrial(number=46, values=[5.825110532660616], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 436573), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 439786), params={'x': -0.41352657591761677}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=46, state=TrialState.COMPLETE, value=None), FrozenTrial(number=47, values=[0.6036993490159309], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 440256), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 443518), params={'x': 1.2230190806616092}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=47, state=TrialState.COMPLETE, value=None), FrozenTrial(number=48, values=[15.375283763917924], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 443987), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 447191), params={'x': 5.921132969425791}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=48, state=TrialState.COMPLETE, value=None), FrozenTrial(number=49, values=[1.4909908767798026], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 447663), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 450868), params={'x': 3.221061373060258}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=49, state=TrialState.COMPLETE, value=None), FrozenTrial(number=50, values=[0.007146077471614382], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 451337), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 454555), params={'x': 2.084534475047843}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=50, state=TrialState.COMPLETE, value=None), FrozenTrial(number=51, values=[0.056323565812320724], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 455030), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 458197), params={'x': 1.7626741358125484}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=51, state=TrialState.COMPLETE, value=None), FrozenTrial(number=52, values=[8.515428918105288], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 458703), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 461879), params={'x': -0.9181207853865967}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=52, state=TrialState.COMPLETE, value=None), FrozenTrial(number=53, values=[4.181142997496314], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 462351), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 465529), params={'x': -0.044784340094650155}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=53, state=TrialState.COMPLETE, value=None), FrozenTrial(number=54, values=[6.964997600024417], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 466001), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 469200), params={'x': 4.639128189388385}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=54, state=TrialState.COMPLETE, value=None), FrozenTrial(number=55, values=[1.2881071423289026], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 469697), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 472921), params={'x': 3.134948079133536}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=55, state=TrialState.COMPLETE, value=None), FrozenTrial(number=56, values=[0.8879128892284678], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 473393), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 476634), params={'x': 1.0577087025614278}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=56, state=TrialState.COMPLETE, value=None), FrozenTrial(number=57, values=[0.0022378989848380205], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 477122), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 480506), params={'x': 2.0473064370338543}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=57, state=TrialState.COMPLETE, value=None), FrozenTrial(number=58, values=[0.049908359522046954], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 480982), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 484209), params={'x': 2.223401789433404}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=58, state=TrialState.COMPLETE, value=None), FrozenTrial(number=59, values=[2.8137188832381823], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 484693), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 487959), params={'x': 3.6774143445309457}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=59, state=TrialState.COMPLETE, value=None), FrozenTrial(number=60, values=[11.194789057557173], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 488437), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 491665), params={'x': 5.345861482123427}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=60, state=TrialState.COMPLETE, value=None), FrozenTrial(number=61, values=[0.09362962132584852], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 492147), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 495378), params={'x': 1.6940104228476915}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=61, state=TrialState.COMPLETE, value=None), FrozenTrial(number=62, values=[2.56241703824846], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 495856), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 499101), params={'x': 0.3992448537491875}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=62, state=TrialState.COMPLETE, value=None), FrozenTrial(number=63, values=[0.7861511281247322], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 499578), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 502825), params={'x': 1.113348361460527}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=63, state=TrialState.COMPLETE, value=None), FrozenTrial(number=64, values=[0.7099653540201463], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 503303), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 506542), params={'x': 2.842594418460119}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=64, state=TrialState.COMPLETE, value=None), FrozenTrial(number=65, values=[0.014753155492807979], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 507032), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 510246), params={'x': 2.1214625682784947}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=65, state=TrialState.COMPLETE, value=None), FrozenTrial(number=66, values=[0.047340616974995295], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 510754), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 513948), params={'x': 2.217578990196653}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=66, state=TrialState.COMPLETE, value=None), FrozenTrial(number=67, values=[5.19906750363538], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 514446), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 517657), params={'x': 4.2801463776774025}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=67, state=TrialState.COMPLETE, value=None), FrozenTrial(number=68, values=[1.9307389261876056], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 518137), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 521382), params={'x': 3.389510318848912}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=68, state=TrialState.COMPLETE, value=None), FrozenTrial(number=69, values=[1.5907470561040322], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 521860), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 525312), params={'x': 0.7387517864813318}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=69, state=TrialState.COMPLETE, value=None), FrozenTrial(number=70, values=[0.34436022812606976], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 525791), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 529082), params={'x': 1.4131778564794357}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=70, state=TrialState.COMPLETE, value=None), FrozenTrial(number=71, values=[0.05794570463000714], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 529558), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 532980), params={'x': 1.7592808594440252}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=71, state=TrialState.COMPLETE, value=None), FrozenTrial(number=72, values=[0.18381754843834092], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 533460), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 536739), params={'x': 2.4287394878458723}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=72, state=TrialState.COMPLETE, value=None), FrozenTrial(number=73, values=[3.7615915269370954], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 537218), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 540521), params={'x': 0.060517716776692154}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=73, state=TrialState.COMPLETE, value=None), FrozenTrial(number=74, values=[9.29401066712111], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 541005), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 544314), params={'x': -1.0486079884303114}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=74, state=TrialState.COMPLETE, value=None), FrozenTrial(number=75, values=[2.6972548738334248], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 544798), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 548087), params={'x': 3.6423321447969728}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=75, state=TrialState.COMPLETE, value=None), FrozenTrial(number=76, values=[0.8936272517073712], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 548568), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 551844), params={'x': 2.945318597990842}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=76, state=TrialState.COMPLETE, value=None), FrozenTrial(number=77, values=[0.007520470076572631], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 552327), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 555622), params={'x': 1.9132793561107124}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=77, state=TrialState.COMPLETE, value=None), FrozenTrial(number=78, values=[55.84913407968906], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 556102), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 559402), params={'x': 9.473227822011655}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=78, state=TrialState.COMPLETE, value=None), FrozenTrial(number=79, values=[0.00886162871555895], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 559886), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 563228), params={'x': 2.0941362242474115}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=79, state=TrialState.COMPLETE, value=None), FrozenTrial(number=80, values=[1.570428164013574], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 563710), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 567005), params={'x': 0.746832746991219}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=80, state=TrialState.COMPLETE, value=None), FrozenTrial(number=81, values=[0.2489317138684525], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 567488), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 570790), params={'x': 2.4989305701883304}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=81, state=TrialState.COMPLETE, value=None), FrozenTrial(number=82, values=[0.006946135798033335], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 571275), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 574554), params={'x': 2.0833434808370357}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=82, state=TrialState.COMPLETE, value=None), FrozenTrial(number=83, values=[119.85869152809477], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 575050), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 578293), params={'x': -8.94799943040256}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=83, state=TrialState.COMPLETE, value=None), FrozenTrial(number=84, values=[0.30055090908184295], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 578817), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 582268), params={'x': 1.4517747642785468}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=84, state=TrialState.COMPLETE, value=None), FrozenTrial(number=85, values=[0.008298851107947676], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 582791), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 586052), params={'x': 1.908901969791067}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=85, state=TrialState.COMPLETE, value=None), FrozenTrial(number=86, values=[0.81238449082439], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 586559), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 589811), params={'x': 2.9013237436262234}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=86, state=TrialState.COMPLETE, value=None), FrozenTrial(number=87, values=[3.4234571855953813], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 590295), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 593640), params={'x': 3.8502586807242336}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=87, state=TrialState.COMPLETE, value=None), FrozenTrial(number=88, values=[5.980567280107914], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 594128), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 597451), params={'x': -0.44551983842043574}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=88, state=TrialState.COMPLETE, value=None), FrozenTrial(number=89, values=[7.5367672156491325], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 597939), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 601251), params={'x': 4.745317325128214}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=89, state=TrialState.COMPLETE, value=None), FrozenTrial(number=90, values=[3.4156371115195874e-06], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 601740), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 605093), params={'x': 2.001848144234501}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=90, state=TrialState.COMPLETE, value=None), FrozenTrial(number=91, values=[0.0005294235941135736], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 605585), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 608920), params={'x': 1.9769907932750046}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=91, state=TrialState.COMPLETE, value=None), FrozenTrial(number=92, values=[0.001699256088845259], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 609412), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 612758), params={'x': 2.0412220340212035}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=92, state=TrialState.COMPLETE, value=None), FrozenTrial(number=93, values=[1.4876265358065823], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 613249), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 616749), params={'x': 0.7803170347149295}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=93, state=TrialState.COMPLETE, value=None), FrozenTrial(number=94, values=[0.3362304167540244], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 617241), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 620583), params={'x': 1.4201462108824119}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=94, state=TrialState.COMPLETE, value=None), FrozenTrial(number=95, values=[3.8072769529169324], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 621073), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 624443), params={'x': 0.0487755247237871}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=95, state=TrialState.COMPLETE, value=None), FrozenTrial(number=96, values=[1.6313980617005581], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 624936), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 628300), params={'x': 3.2772619393454727}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=96, state=TrialState.COMPLETE, value=None), FrozenTrial(number=97, values=[0.33653518497034546], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 628794), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 632141), params={'x': 2.5801165270618873}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=97, state=TrialState.COMPLETE, value=None), FrozenTrial(number=98, values=[0.0064686857917867985], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 632641), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 635990), params={'x': 1.9195718594533804}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=98, state=TrialState.COMPLETE, value=None), FrozenTrial(number=99, values=[2.2208685778175004], datetime_start=datetime.datetime(2022, 7, 1, 1, 26, 56, 636486), datetime_complete=datetime.datetime(2022, 7, 1, 1, 26, 56, 639836), params={'x': 0.5097421102985227}, distributions={'x': UniformDistribution(high=10.0, low=-10.0)}, 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: 2.001848144234501, (x - 2)^2: 3.4156371115195874e-06
Total running time of the script: ( 0 minutes 0.772 seconds)