Use hypervolume difference as upperbound of contribs in HSSP #6131
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not522
added
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nabenabe0928
reviewed
Jun 5, 2025
optuna/_hypervolume/hssp.py
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| # Note: H(T v {j}) - H(T) <= H({t} v {j}) - H({t}) = H({j}) - H({t} ^ {j}). | ||
| # Here, t is the last selected point and j is the candidate. The inequality comes from | ||
| # submodularity and the equality comes from the inclusion-exclusion principle. | ||
| single_volume = np.abs(np.prod(pareto_loss_values - reference_point[np.newaxis, :], axis=1)) |
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We could precompute single_volume if necessary.
It is an implicit assumption, but the compute_hypervolume function internally checks np.all(pareto_loss_values <= reference_point[np.newaxis, :]), so np.prod(reference_point[np.newaxis, :] - pareto_loss_values, axis=1) is equivalent.
Note
r - a is quicker than r[np.newaxis, :] - a.
In [1]: import numpy as np
...:
...:
...: a = np.random.random((30, 3))
...: r = np.ones(3)
...: %timeit r - a
...: %timeit r[np.newaxis, :] - a
...: assert np.allclose(r - a, r[np.newaxis, :] - a)
708 ns ± 8.28 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
887 ns ± 10.7 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
|
I confirmed the reproducibility with the following! contribs = np.minimum(
contribs,
(
np.prod(reference_point - pareto_loss_values, axis=1)
- np.prod(reference_point - np.maximum(selected_vecs[-2], pareto_loss_values), axis=1)
),
) |
Co-authored-by: Shuhei Watanabe <[email protected]>
Codecov ReportAll modified and coverable lines are covered by tests ✅
Additional details and impacted files@@ Coverage Diff @@
## master #6131 +/- ##
==========================================
+ Coverage 88.29% 88.42% +0.13%
==========================================
Files 207 207
Lines 14034 14043 +9
==========================================
+ Hits 12391 12418 +27
+ Misses 1643 1625 -18 ☔ View full report in Codecov by Sentry. |
Co-authored-by: Shuhei Watanabe <[email protected]>
nabenabe0928
reviewed
Jun 6, 2025
Co-authored-by: Shuhei Watanabe <[email protected]>
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Motivation
Since
contribsin HSSP manages the upper bound of contribution for each point, it can be updated by the difference HV with the last selected point and the next candidate. This reduces the number of points that actually require hypervolume calculation.Description of the changes
Benchmark