def METHOD_NAME(capsys: _pytest.capture.CaptureFixture) -> None:
    # We need to reconstruct our default handler to properly capture stderr.
    optuna.logging._reset_library_root_logger()
    optuna.logging.set_verbosity(optuna.logging.INFO)
    study = optuna.multi_objective.create_study(["minimize", "maximize"])
    study.optimize(lambda t: (1.0, 1.0), n_trials=1)
    _, err = capsys.readouterr()
    assert "Trial 0" in err
    optuna.logging.set_verbosity(optuna.logging.WARNING)
    study.optimize(lambda t: (1.0, 1.0), n_trials=1)
    _, err = capsys.readouterr()
    assert "Trial 1" not in err
    optuna.logging.set_verbosity(optuna.logging.DEBUG)
    study.optimize(lambda t: (1.0, 1.0), n_trials=1)
    _, err = capsys.readouterr()
    assert "Trial 2" in err