fix get_default_partitioning_alpha for >7 objectives (#2646)

Summary:
Pull Request resolved: #2646

This ensures the approximation hyperparameter (alpha) for approximate box decompositions is less than 1.

Reviewed By: esantorella

Differential Revision: D66834901

fbshipit-source-id: d5eb8c9cbd8969fe27fb3a01e5dd192de9ab978a

botorch/acquisition/multi_objective/utils.py

@@ -60,7 +60,7 @@ def get_default_partitioning_alpha(num_objectives: int) -> float:
             BotorchWarning,
             stacklevel=3,
         )
-    return 10 ** (-8 + num_objectives)
+    return 10 ** (-2 if num_objectives >= 6 else -3)
 
 
 def prune_inferior_points_multi_objective(

test/acquisition/multi_objective/test_utils.py

@@ -32,16 +32,16 @@
 
 class TestUtils(BotorchTestCase):
     def test_get_default_partitioning_alpha(self):
-        for m in range(2, 7):
-            expected_val = 0.0 if m < 5 else 10 ** (-8 + m)
+        for m in range(2, 9):
+            expected_val = 0.0 if m < 5 else 10 ** (-2 if m >= 6 else -3)
             self.assertEqual(
                 expected_val, get_default_partitioning_alpha(num_objectives=m)
             )
         # In `BotorchTestCase.setUp` warnings are filtered, so here we
         # remove the filter to ensure a warning is issued as expected.
         warnings.resetwarnings()
         with warnings.catch_warnings(record=True) as ws:
-            self.assertEqual(0.1, get_default_partitioning_alpha(num_objectives=7))
+            self.assertEqual(0.01, get_default_partitioning_alpha(num_objectives=7))
         self.assertEqual(len(ws), 1)