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Add log-linear algorithm for 2d Pareto front. #2503

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merged 5 commits into from Mar 25, 2021
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Add log-linear algorithm for 2d Pareto front. #2503

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11b5187
Add log-linear algorithm for 2d Pareto front.
parsiad Mar 20, 2021
54c51a6
Add edge case to 2d Pareto front algorithm.
parsiad Mar 21, 2021
0fbc94a
Use _dominates in 2d Pareto front algorithm.
parsiad Mar 24, 2021
846b78f
Add 3d Pareto front test case.
parsiad Mar 24, 2021
ab17d55
Remove mask from 2d Pareto front algorithm.
parsiad Mar 24, 2021
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47 changes: 46 additions & 1 deletion optuna/_multi_objective.py
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Expand Up @@ -8,7 +8,46 @@
from optuna.trial import TrialState


def _get_pareto_front_trials(study: "optuna.study.BaseStudy") -> List[FrozenTrial]:
def _get_pareto_front_trials_2d(study: "optuna.study.BaseStudy") -> List[FrozenTrial]:
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How about sorting the trials themself, and using _dominates function as done in _get_pareto_front_trials_nd?

    pareto_front = []
    trials = [trial for trial in study.trials if trial.state == TrialState.COMPLETE]
    trials.sort(key=lambda t: _normalize_value(t.values[1], study.directions[1]))
    trials.sort(key=lambda t: _normalize_value(t.values[0], study.directions[0]))

    last_nondominated_trial: Optional[FrozenTrial] = None
    for i in range(len(trials)):
        if i == 0:
            pareto_front.append(trials[0])
            last_nondominated_trial = trials[0]
            continue

        assert last_nondominated_trial is not None
        if not _dominates(last_nondominated_trial, trials[i], study.directions):
            pareto_front.append(trials[i])
            last_nondominated_trial = trials[i]

This code does not preserve the order of all trials and pareto front trials. so it will be fixed.

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@parsiad parsiad Mar 24, 2021 •
edited

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I like the idea of using _dominates to simplify the code. I implemented your suggestion.

The only difference between my implementation and your suggestion is that I am still using mask because the order of trials needs to be preserved when filtering (as you point out in your comment).

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To preserve the order of trials, we only need to sort the Pareto front trials with its trial.number. Could you remove the mask? (I have noticed this simple fix after posting the above messages. Sorry.)

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Nice catch. Done.

trials = [trial for trial in study.trials if trial.state == TrialState.COMPLETE]
points = sorted(
(
+_normalize_value(trial.values[0], study.directions[0]),
-_normalize_value(trial.values[1], study.directions[1]),
index,
)
for index, trial in enumerate(trials)
)

mask = [False] * len(trials)

def set_mask(width: int, hi: int) -> None:
for k in range(hi - width, hi):
_, _, index = points[k]
mask[index] = True

width = 0
best_y = float("inf")
curr_x = float("nan")
for i, (x, y, _) in enumerate(points):
y = -y
if curr_x != x:
set_mask(width, hi=i)
width = 0
if y > best_y or (y == best_y and width == 0):
continue
if y < best_y:
width = 0
width += 1
best_y = y
curr_x = x
set_mask(width, hi=len(points))

pareto_front = [trial for trial, keep in zip(trials, mask) if keep]
return pareto_front


def _get_pareto_front_trials_nd(study: "optuna.study.BaseStudy") -> List[FrozenTrial]:
pareto_front = []
trials = [t for t in study.trials if t.state == TrialState.COMPLETE]

Expand All @@ -26,6 +65,12 @@ def _get_pareto_front_trials(study: "optuna.study.BaseStudy") -> List[FrozenTria
return pareto_front


def _get_pareto_front_trials(study: "optuna.study.BaseStudy") -> List[FrozenTrial]:
if len(study.directions) == 2:
return _get_pareto_front_trials_2d(study) # Log-linear in number of trials.
return _get_pareto_front_trials_nd(study) # Quadratic in number of trials.
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The non-2d scenario seems not to be covered by any test case in test_study.py. We may want to add new ones, since it's risky to leave the general logic not tested.

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@parsiad parsiad Mar 24, 2021 •
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Added a 3d test case.



def _dominates(
trial0: FrozenTrial, trial1: FrozenTrial, directions: Sequence[StudyDirection]
) -> bool:
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3 changes: 3 additions & 0 deletions tests/study_tests/test_study.py
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Expand Up @@ -831,6 +831,9 @@ def _trial_to_values(t: FrozenTrial) -> Tuple[float, ...]:
study.optimize(lambda t: [3, 1], n_trials=1)
assert {_trial_to_values(t) for t in study.best_trials} == {(1, 1), (2, 2)}

study.optimize(lambda t: [3, 2], n_trials=1)
assert {_trial_to_values(t) for t in study.best_trials} == {(1, 1), (2, 2)}

study.optimize(lambda t: [1, 3], n_trials=1)
assert {_trial_to_values(t) for t in study.best_trials} == {(1, 3)}
assert len(study.best_trials) == 1
Expand Down