def _update_pareto_Y(self) -> bool:
r"""Update the non-dominated front.
Returns:
A boolean indicating whether the Pareto frontier has changed.
"""
# is_non_dominated assumes maximization
if self._neg_Y.shape[-2] == 0:
pareto_Y = self._neg_Y
else:
# assumes maximization
pareto_Y = -_pad_batch_pareto_frontier(
Y=self.Y,
ref_point=_expand_ref_point(
ref_point=self.ref_point, batch_shape=self.batch_shape
),
)
if self.sort:
# sort by first objective
if len(self.batch_shape) > 0:
pareto_Y = pareto_Y.gather(
index=torch.argsort(pareto_Y[..., :1], dim=-2).expand(
pareto_Y.shape
),
dim=-2,
)
else:
pareto_Y = pareto_Y[torch.argsort(pareto_Y[:, 0])]
if not hasattr(self, "_neg_pareto_Y") or not torch.equal(
pareto_Y, self._neg_pareto_Y
):
self.register_buffer("_neg_pareto_Y", pareto_Y)
return True
return False
def get_hypercell_bounds(self) -> Tensor:
r"""Get the bounds of each hypercell in the decomposition.
Args:
ref_point: A `(batch_shape) x m`-dim tensor containing the reference point.
Returns:
A `2 x num_cells x num_outcomes`-dim tensor containing the
lower and upper vertices bounding each hypercell.
"""
ref_point = _expand_ref_point(ref_point=self.ref_point,
batch_shape=self.batch_shape)
aug_pareto_Y = torch.cat(
[
# -inf is the lower bound of the non-dominated space
torch.full(
torch.Size([
*self.batch_shape,
1,
self.num_outcomes,
]),
float("-inf"),
dtype=self._neg_pareto_Y.dtype,
device=self._neg_pareto_Y.device,
),
self._neg_pareto_Y,
# note: internally, this class minimizes, so use negative here
-(ref_point.unsqueeze(-2)),
],
dim=-2,
)
minimization_cell_bounds = self._get_hypercell_bounds(
aug_pareto_Y=aug_pareto_Y)
# swap upper and lower bounds and multiply by -1
return -minimization_cell_bounds.flip(0)
def compute_hypervolume(self) -> Tensor:
r"""Compute the hypervolume for the given reference point.
This method computes the hypervolume of the non-dominated space
and computes the difference between the hypervolume between the
ideal point and hypervolume of the non-dominated space.
Returns:
`(batch_shape)`-dim tensor containing the dominated hypervolume.
"""
if self._neg_pareto_Y.shape[-2] == 0:
return torch.zeros(
self._neg_pareto_Y.shape[:-2],
dtype=self._neg_pareto_Y.dtype,
device=self._neg_pareto_Y.device,
)
ref_point = _expand_ref_point(ref_point=self.ref_point,
batch_shape=self.batch_shape)
# internally we minimize
ref_point = -ref_point.unsqueeze(-2)
ideal_point = self._neg_pareto_Y.min(dim=-2, keepdim=True).values
aug_pareto_Y = torch.cat([ideal_point, self._neg_pareto_Y, ref_point],
dim=-2)
cell_bounds_values = self._get_hypercell_bounds(
aug_pareto_Y=aug_pareto_Y)
total_volume = (ref_point - ideal_point).squeeze(-2).prod(dim=-1)
non_dom_volume = ((cell_bounds_values[1] -
cell_bounds_values[0]).prod(dim=-1).sum(dim=-1))
return total_volume - non_dom_volume
def test_expand_ref_point(self):
ref_point = torch.tensor([1.0, 2.0], device=self.device)
for dtype in (torch.float, torch.double):
ref_point = ref_point.to(dtype=dtype)
# test non-batch
self.assertTrue(
torch.equal(
_expand_ref_point(ref_point, batch_shape=torch.Size([])),
ref_point,
))
self.assertTrue(
torch.equal(
_expand_ref_point(ref_point, batch_shape=torch.Size([3])),
ref_point.unsqueeze(0).expand(3, -1),
))
# test ref point with wrong shape batch_shape
with self.assertRaises(BotorchTensorDimensionError):
_expand_ref_point(ref_point.unsqueeze(0),
batch_shape=torch.Size([]))
with self.assertRaises(BotorchTensorDimensionError):
_expand_ref_point(
ref_point.unsqueeze(0).expand(3, -1), torch.Size([2]))