optuna.visualization.plot_edf(study, *, target=None, target_name='Objective Value')[source]

Plot the objective value EDF (empirical distribution function) of a study.

Note that only the complete trials are considered when plotting the EDF.


EDF is useful to analyze and improve search spaces. For instance, you can see a practical use case of EDF in the paper Designing Network Design Spaces.


The plotted EDF assumes that the value of the objective function is in accordance with the uniform distribution over the objective space.


The following code snippet shows how to plot EDF.

import math

import optuna

def ackley(x, y):
    a = 20 * math.exp(-0.2 * math.sqrt(0.5 * (x ** 2 + y ** 2)))
    b = math.exp(0.5 * (math.cos(2 * math.pi * x) + math.cos(2 * math.pi * y)))
    return -a - b + math.e + 20

def objective(trial, low, high):
    x = trial.suggest_float("x", low, high)
    y = trial.suggest_float("y", low, high)
    return ackley(x, y)

sampler = optuna.samplers.RandomSampler(seed=10)

# Widest search space.
study0 = optuna.create_study(study_name="x=[0,5), y=[0,5)", sampler=sampler)
study0.optimize(lambda t: objective(t, 0, 5), n_trials=500)

# Narrower search space.
study1 = optuna.create_study(study_name="x=[0,4), y=[0,4)", sampler=sampler)
study1.optimize(lambda t: objective(t, 0, 4), n_trials=500)

# Narrowest search space but it doesn't include the global optimum point.
study2 = optuna.create_study(study_name="x=[1,3), y=[1,3)", sampler=sampler)
study2.optimize(lambda t: objective(t, 1, 3), n_trials=500)

fig = optuna.visualization.plot_edf([study0, study1, study2])
  • study (Study | Sequence[Study]) – A target Study object. You can pass multiple studies if you want to compare those EDFs.

  • target (Callable[[FrozenTrial], float] | None) –

    A function to specify the value to display. If it is None and study is being used for single-objective optimization, the objective values are plotted.


    Specify this argument if study is being used for multi-objective optimization.

  • target_name (str) – Target’s name to display on the axis label.


A plotly.graph_objects.Figure object.

Return type: