Yes, Ax can handle using hierarchical search spaces in multi objective optimization. Ax handles this by flattening down the space during the transformations that take place before the values reach botorch. This functionality is rather new and not fully supported yet so you may run into some difficulty, but we're happy to help you out as best we can.

Since this functionality is so new there is no tutorial on our website, but I've thrown together this little snippet that should help you get started on your own.

from ax.service.ax_client import AxClient
from ax.service.utils.instantiation import ObjectiveProperties

ax_client = AxClient()
ax_client.create_experiment(
    name="moo_experiment",
    parameters=[
        {
            "name": "model",
            "type": "choice",
            "values": ['Linear', 'XGBoost'],
            "dependents": {'Linear': ['learning_rate', 'l2_reg_weight'], 'XGBoost': ['num_boost_rounds']}
        },
        {
            "name": "learning_rate",
            "type": "range",
            "bounds": [0.001, 0.1]
        },
        {
            "name": "l2_reg_weight",
            "type": "range",
            "bounds": [1e-05, 0.001]
        },
        {
            "name": "num_boost_rounds",
            "type": "range",
            "value_type": "int",
            "bounds": [10, 20]
        },
    ],
    objectives={
        "a": ObjectiveProperties(minimize=False), 
        "b": ObjectiveProperties(minimize=False)
    },
)

Does botorch optimizer in mo setting such as qehvi, qnehvi or qnparego support hierarchical space? #1042

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