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: 2.0057661877093325, (x - 2)^2: 3.324892069925672e-05
We can see that the x value found by Optuna is close to the optimal value of 2.
Note
When used to search for hyperparameters in machine learning, usually the objective function would return the loss or accuracy of the model.
Study Object
Let us clarify the terminology in Optuna as follows:
Trial: A single call of the objective function
Study: An optimization session, which is a set of trials
Parameter: A variable whose value is to be optimized, such as
xin the above example
In Optuna, we use the study object to manage optimization.
Method create_study() returns a study object.
A study object has useful properties for analyzing the optimization outcome.
To get the dictionary of parameter name and parameter values:
study.best_params
{'x': 2.0057661877093325}
To get the best observed value of the objective function:
study.best_value
3.324892069925672e-05
To get the best trial:
study.best_trial
FrozenTrial(number=90, values=[3.324892069925672e-05], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 109821), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 113204), params={'x': 2.0057661877093325}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=90, state=TrialState.COMPLETE, value=None)
To get all trials:
study.trials
[FrozenTrial(number=0, values=[113.38189877558646], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 803392), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 803820), params={'x': -8.648093668614418}, 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=[21.82567300557696], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 804266), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 804545), params={'x': -2.671795479853218}, 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=[0.17666828229199863], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 804940), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 805193), params={'x': 1.5796807376624304}, 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=[1.8068495185606144], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 805584), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 805829), params={'x': 0.655808972444536}, 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=[24.870041887781543], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 806234), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 806488), params={'x': 6.986987255626541}, 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=[9.23580124073716], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 806903), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 807156), params={'x': 5.039046107043649}, 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=[9.518762188149354], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 807543), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 807802), params={'x': -1.085249129024973}, 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=[0.00016911669605590394], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 808186), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 808442), params={'x': 2.013004487535305}, 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=[77.83356474090665], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 808829), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 809093), params={'x': -6.822333293460787}, 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=[9.659650060975473], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 809469), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 809732), params={'x': 5.107997757556378}, 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=[60.57357467622945], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 810122), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 813704), params={'x': 9.78290271532604}, 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=[0.025153884332110403], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 814300), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 817375), params={'x': 1.8414002385496422}, 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=[35.21073790295108], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 817838), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 821286), params={'x': -3.933863657260005}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=12, state=TrialState.COMPLETE, value=None), FrozenTrial(number=13, values=[0.8832890494560314], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 821765), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 824856), params={'x': 2.939834586220379}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=13, state=TrialState.COMPLETE, value=None), FrozenTrial(number=14, values=[0.7939515167676111], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 825335), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 828458), params={'x': 2.8910395708202925}, 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=[39.37866110405093], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 828938), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 832030), params={'x': -4.2752419159782935}, 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=[8.474514377410497], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 832500), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 835586), params={'x': -0.9111019180733773}, 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=[30.417256966540716], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 836057), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 839125), params={'x': 7.515184218731113}, 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=[4.270625723265451], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 839583), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 842674), params={'x': 4.0665492307867845}, 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=[1.0006722463078717], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 843140), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 846235), params={'x': 0.9996639333164721}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=19, state=TrialState.COMPLETE, value=None), FrozenTrial(number=20, values=[13.04820676599441], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 846743), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 849801), params={'x': -1.6122301651465134}, 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=[0.10266620827222236], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 850307), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 853394), params={'x': 1.679584319559385}, 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=[0.0687577732566218], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 853861), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 856971), params={'x': 2.2622170346423394}, 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=[22.47080605803748], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 857444), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 860582), params={'x': 6.740338179712232}, 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=[1.580440707367104], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 861058), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 864205), params={'x': 3.2571558007530745}, 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=[2.9192499439805273], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 864677), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 867804), params={'x': 0.2914187335743941}, 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=[10.634096581835736], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 868279), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 871408), params={'x': 5.260996256029089}, 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=[0.030783668496590602], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 871885), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 875021), params={'x': 2.175452752889747}, 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=[23.137389108915045], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 875485), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 878648), params={'x': -2.8101340011391622}, 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=[113.77281248315174], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 879119), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 882256), params={'x': -8.666433915941717}, 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=[70.73266716512317], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 882750), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 885855), params={'x': -6.410271527431393}, 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=[0.19949633871492742], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 886338), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 890111), params={'x': 2.446650130096172}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=31, state=TrialState.COMPLETE, value=None), FrozenTrial(number=32, values=[4.588260808274755], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 890631), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 893770), params={'x': 4.142022597517299}, 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=[3.6666295179208945], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 894252), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 897508), params={'x': 0.0851554846617717}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=33, state=TrialState.COMPLETE, value=None), FrozenTrial(number=34, values=[0.028636450922285204], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 898004), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 901231), params={'x': 1.8307769196525332}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=34, state=TrialState.COMPLETE, value=None), FrozenTrial(number=35, values=[0.2214781158364663], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 901711), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 904938), params={'x': 1.5293853850160768}, 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=[18.597028237901906], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 905434), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 908684), params={'x': -2.3124271863884154}, 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=[6.351764730315756], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 909162), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 912356), params={'x': -0.5202707652781586}, 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=[3.3277458399976942], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 912825), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 916037), params={'x': 3.8242110184947613}, 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=[16.08785467634024], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 916498), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 919722), params={'x': 6.010966800702823}, 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=[37.69006309922584], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 920180), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 923390), params={'x': 8.139223330293975}, 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=[0.026760619843468992], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 923856), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 927072), params={'x': 2.163586734925143}, 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=[0.8251694551137538], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 927546), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 930765), params={'x': 1.0916116165902638}, 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=[3.9756886297872445], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 931228), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 934809), params={'x': 0.006087105767344614}, 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=[7.127810718655357e-05], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 935279), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 938473), params={'x': 1.9915573637300572}, 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=[5.248508324824732], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 938961), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 942148), params={'x': 4.29096231414328}, 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=[0.7273888118748257], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 942636), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 945844), params={'x': 1.147129076662344}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=46, state=TrialState.COMPLETE, value=None), FrozenTrial(number=47, values=[1.6640619040739042], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 946353), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 949610), params={'x': 3.289985234052663}, 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=[9.33805929491345], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 950117), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 953363), params={'x': -1.0558238324408442}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=48, state=TrialState.COMPLETE, value=None), FrozenTrial(number=49, values=[10.907390675210534], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 953860), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 957099), params={'x': 5.302633899664105}, 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=[0.013882611762036144], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 957575), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 960815), params={'x': 2.117824495594236}, 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=[0.006137200074982712], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 961287), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 964540), params={'x': 1.921659716141804}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=51, state=TrialState.COMPLETE, value=None), FrozenTrial(number=52, values=[1.602581362141744], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 965007), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 968272), params={'x': 0.734068974176814}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=52, state=TrialState.COMPLETE, value=None), FrozenTrial(number=53, values=[2.178777346035803], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 968741), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 972179), params={'x': 3.476068205075837}, 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=[0.667033168816571], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 972661), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 975957), params={'x': 2.8167209859043485}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=54, state=TrialState.COMPLETE, value=None), FrozenTrial(number=55, values=[6.672538848862622], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 976445), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 979757), params={'x': 4.583125790367674}, 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=[15.229528510355443], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 980256), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 983557), params={'x': -1.9025028520624354}, 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=[6.100899433833179], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 984050), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 987339), params={'x': -0.4699998853913292}, 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=[0.04282501065939852], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 987826), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 991173), params={'x': 2.2069420466203002}, 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=[1.6664989752133619], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 991647), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 994906), params={'x': 0.7090704995185206}, 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=[0.561268194612212], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 995387), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 46, 998651), params={'x': 2.749178346331641}, 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=[0.11850953680201615], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 46, 999132), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 2373), params={'x': 1.6557478586820176}, 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=[0.008559911271883335], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 2905), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 6215), params={'x': 1.9074802114578544}, 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=[0.49967355647299017], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 6769), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 10079), params={'x': 1.29312408693393}, 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=[2.4592954189785203], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 10632), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 13884), params={'x': 3.5682140858245472}, 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=[7.891382590507665], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 14410), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 17677), params={'x': 4.809160477884392}, 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=[2.544792830958518], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 18184), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 21441), params={'x': 0.40475931879903526}, 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=[0.09749376133569], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 21930), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 25176), params={'x': 2.3122399099021296}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=67, state=TrialState.COMPLETE, value=None), FrozenTrial(number=68, values=[5.901622426669667], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 25664), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 28957), params={'x': -0.42932550858662566}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=68, state=TrialState.COMPLETE, value=None), FrozenTrial(number=69, values=[0.015329748008513918], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 29451), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 32768), params={'x': 1.8761866404279655}, 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=[1.1425995099995556], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 33256), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 36568), params={'x': 3.0689244641224915}, 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=[0.24314328493509405], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 37055), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 40344), params={'x': 1.5069043856054953}, 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=[0.08340941919139087], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 40821), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 44107), params={'x': 2.288806889099604}, 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=[0.014654371347422578], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 44586), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 47881), params={'x': 1.87894475910799}, 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=[141.22840608257792], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 48359), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 51664), params={'x': -9.883955826347467}, 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=[1.2454741929733861], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 52155), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 55463), params={'x': 0.8839918490560268}, 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=[3.844514530886119], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 55941), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 59226), params={'x': 3.9607433618110552}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=76, state=TrialState.COMPLETE, value=None), FrozenTrial(number=77, values=[0.6096864910239392], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 59701), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 63033), params={'x': 2.7808242382405526}, 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=[2.934301492785796], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 63527), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 66939), params={'x': 0.2870197044957592}, 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=[0.0056804787670967855], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 67542), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 70845), params={'x': 1.9246310490513714}, 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=[0.06534976990711343], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 71325), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 74944), params={'x': 1.7443639894163707}, 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=[0.47463154221350423], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 75425), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 78707), params={'x': 1.3110649216264973}, 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=[0.014202605529967405], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 79181), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 82514), params={'x': 1.880825315062437}, 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=[0.012120398798895366], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 83046), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 86349), params={'x': 1.8899073172327272}, 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=[0.42583027395513906], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 86856), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 90149), params={'x': 2.65255672087194}, 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=[4.878834777499532], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 90659), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 93982), params={'x': -0.20880845197122788}, distributions={'x': FloatDistribution(high=10.0, log=False, low=-10.0, step=None)}, user_attrs={}, system_attrs={}, intermediate_values={}, trial_id=85, state=TrialState.COMPLETE, value=None), FrozenTrial(number=86, values=[2.604326424567017], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 94466), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 97773), params={'x': 3.613792559335622}, 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=[2.104389551525081], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 98276), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 101636), params={'x': 0.549348576836916}, 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=[11.007351048986852], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 102137), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 105496), params={'x': -1.317732817601027}, 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=[13.408950914512008], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 106003), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 109330), params={'x': 5.661823441198662}, 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=[3.324892069925672e-05], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 109821), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 113204), params={'x': 2.0057661877093325}, 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=[1.337515143257826], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 113703), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 117060), params={'x': 3.156509897604783}, 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=[0.007768149887881046], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 117555), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 120924), params={'x': 1.911862891538915}, 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=[0.9125328813108313], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 121410), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 125347), params={'x': 1.0447341305632074}, 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=[0.10730720012574581], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 125838), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 129174), params={'x': 2.327577777215955}, 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=[5.321529601147536], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 129799), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 133248), params={'x': 4.30684407820458}, 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=[0.42164147069340296], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 133742), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 137121), params={'x': 1.3506607429906898}, 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=[1.246969577387635], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 137615), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 141307), params={'x': 3.116677920166614}, 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=[8.073485829831771], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 141801), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 145189), params={'x': -0.8413880111367704}, 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=[1.363730332420454], datetime_start=datetime.datetime(2022, 10, 11, 7, 18, 47, 145676), datetime_complete=datetime.datetime(2022, 10, 11, 7, 18, 47, 149028), params={'x': 0.8322113494212859}, 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: 2.0041165478356304, (x - 2)^2: 1.694596608303353e-05
Total running time of the script: ( 0 minutes 0.786 seconds)