optuna_suggest_normal.py

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import norm
from scipy.special import erfcinv

import optuna


def objective(trial):
    # Suggest from U(0, 1) with Optuna.
    x = trial.suggest_float("x", 0, 1)

    # Inverse transform into normal.
    y0 = norm.ppf(x, loc=0, scale=1)

    # Inverse transform into lognormal.
    y1 = np.exp(-np.sqrt(2) * erfcinv(2 * x))

    return y0, y1


if __name__ == "__main__":
    n_objectives = 2  # Normal and lognormal.

    study = optuna.create_study(
        sampler=optuna.samplers.RandomSampler(),
        # Could be "maximize". Does not matter for this demonstration.
        directions=["minimize"] * n_objectives,
    )
    study.optimize(objective, n_trials=10000)

    fig, axs = plt.subplots(n_objectives)
    for i in range(n_objectives):
        axs[i].hist(list(t.values[i] for t in study.trials), bins=100)
    plt.show()

Resulting plots.