Best parameters of an Optuna multi-objective optimization

Question

When performing a single-objective optimization with Optuna, the best parameters of the study are accessible using:

import optuna
def objective(trial):
    x = trial.suggest_uniform('x', -10, 10)
    return (x - 2) ** 2

study = optuna.create_study(direction='minimize')
study.optimize(objective, n_trials=100)

study.best_params  # E.g. {'x': 2.002108042}

If I want to perform a multi-objective optimization, this would be become for example :

import optuna
def multi_objective(trial):
    x = trial.suggest_uniform('x', -10, 10)
    f1 = (x - 2) ** 2
    f2 = -f1
    return f1, f2

study = optuna.create_study(directions=['minimize', 'maximize'])
study.optimize(multi_objective, n_trials=100)

This works, but the command study.best_params fails with RuntimeError: The best trial of a 'study' is only supported for single-objective optimization.

How can I get the best parameters for a multi-objective optimization ?

hvy · Accepted Answer · 2021-01-21 23:56:09Z

10

In multi-objective optimization, you often end up with more than one best trial, but rather a set of trials. This set if often referred to as the Pareto front. You can get this Pareto front, or the list of trials, via study.best_trials, then look at the parameters from each individual trial i.e. study.best_trials[some_index].params.

For instance, given your directions of minimizing f1 and maximizing f2, you might end up with a trial that has a small value for f1 (good) but at the same time small value for f2 (bad) while another trial might have a large value for both f1 (bad) and f2 (good). Both of these trials could be returned from study.best_trials.

answered Jan 21, 2021 at 23:56

hvy

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3 Comments

Dr. Paprika Over a year ago

Are there any guidlines on how to choose between all the trials in study.best_trials ?

hvy Over a year ago

If the number of objectives is either two or three, you can use of optuna.visualization.plot_pareto_front to plot the Pareto front for visual inspection. This requires plotly. Beyond that, for the time being is outside the scope of Optuna. It is a topic of research in my understanding.

Cyril Over a year ago

@Dr.Paprika the answer depends of your problem. You can get the best_params_ and filter on the first value then the second one, or the opposite. You could be more strict on the first parameter but not on the second. Clearly that depends of you and what you want at the end.

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