Clamp to 0 to avoid sqrt of negative numbers in mvn_hellinger_distance (#3109)

Summary:
## Motivation

When trying out ScoreBO, I noticed that it tended to explore excessively. I found that the acquisition function occasionally contained NaNs that originated from the mvn_hellinger_distance function. When computing 1 - x.exp() for small x, the result is sometimes negative due to floating point inaccuriacies which causes the sqrt to output NaN.

### Have you read the [Contributing Guidelines on pull requests](https://github.com/meta-pytorch/botorch/blob/main/CONTRIBUTING.md#pull-requests)?

Yes.

Pull Request resolved: #3109

Test Plan: The change is rather minor but I've added a test to `test_community/utils/test_stat_dist.py`.

Reviewed By: saitcakmak

Differential Revision: D88863196

Pulled By: hvarfner

fbshipit-source-id: a5f72db77143c0e1c43a784f6e0b24b33a9b2e36

Author: Jack-Sandberg

botorch_community/utils/stat_dist.py

@@ -85,4 +85,4 @@ def mvn_hellinger_distance(
     L_mean_diff = torch.matmul(L_inv, mean_diff)
     exp_logterm = -0.125 * torch.matmul(L_mean_diff.transpose(-2, -1), L_mean_diff)
     sq_hdist = 1 - (base_logterm + exp_logterm.squeeze(-1)).exp()
-    return sq_hdist.sqrt()
+    return sq_hdist.clamp_min(0.0).sqrt()

test_community/utils/test_stat_dist.py

@@ -76,3 +76,14 @@ def test_mvn_hellinger_distance(self):
         )
         self.assertTrue(torch.all(permean_res > 0))
         self.assertTrue(torch.all(percov_res > 0))
+
+    def test_mvn_hellinger_distance_numerical_stability(self):
+        # Two almost equal distributions. Distance is approximatly 0.
+        dist1_mean = torch.tensor([[-0.4615126826879162]], dtype=torch.float64)
+        dist2_mean = torch.tensor([[-0.46151268268791173]], dtype=torch.float64)
+        dist1_cov = torch.tensor([[0.12132352941175625]], dtype=torch.float64)
+        dist2_cov = torch.tensor([[0.12132352941176472]], dtype=torch.float64)
+
+        res = mvn_hellinger_distance(dist1_mean, dist2_mean, dist1_cov, dist2_cov)
+        self.assertFalse(res.isnan().any())
+        self.assertAllClose(res, torch.tensor([0.0], dtype=torch.float64))