speed up LCE-A kernel (#1910)

Summary:
Pull Request resolved: #1910

X-link: facebook/Ax#1694

The current implementation is very slow. This is particularly problematic when the number of contexts is large.

This diff yields huge speed ups (>3 orders of magnitude) by removing nested for loops in `forward` and instead using batched computation. This also caches the context_covar in eval mode, with an additional requirements that the parameters for each context are contiguous and in the same order.

* 14x speed up with 8 contexts and 1,154x speed up with 128 contexts (CPU)

* 22x speed up with 8 contexts and 3,370x speed up with 128 contexts (CUDA)
* Without this diff, it takes 5 seconds on CPU and 12 seconds with CUDA for a single forward pass with 128 contexts.

Current implementation:

* 8 contexts:
  * Forward pass: 20ms (CPU), 45.2ms (CUDA)
  * Roundtrip: 39.1ms (CPU), 99.7ms (CUDA)
* 128 contexts:
  * Forward pass: 5.08s (CPU), 12s (CUDA)
  * Roundtrip: 14.2s (CPU), 26.7s (CUDA)

New Implementation:
* 8 contexts:
  * Forward pass: 1.44ms (CPU), 2.05ms (CUDA)
  * Roundtrip: 2.22ms (CPU), 4.65ms (CUDA)
* 128 contexts:
  * Forward pass: 4.4ms (CPU), 3.56ms (CUDA)
  * Roundtrip: 6.97ms (CPU), 5.34ms (CUDA)

Reviewed By: Balandat

Differential Revision: D47118335

fbshipit-source-id: efa091bf7ccc30559d921195e10c1375f525cca9

botorch/models/contextual.py

@@ -66,8 +66,7 @@ def __init__(
             train_Y: (n x 1) Y training data.
             train_Yvar: (n x 1) Noise variance of Y.
             decomposition: Keys are context names. Values are the indexes of
-                parameters belong to the context. The parameter indexes are in the
-                same order across contexts.
+                parameters belong to the context.
             cat_feature_dict: Keys are context names and values are list of categorical
                 features i.e. {"context_name" : [cat_0, ..., cat_k]}, where k is the
                 number of categorical variables. If None, we use context names in the

botorch/models/kernels/contextual_lcea.py

@@ -11,11 +11,78 @@
 from gpytorch.kernels.kernel import Kernel
 from gpytorch.kernels.matern_kernel import MaternKernel
 from gpytorch.priors.torch_priors import GammaPrior
-from linear_operator.operators.sum_linear_operator import SumLinearOperator
+from linear_operator.operators import DiagLinearOperator
+from linear_operator.operators.dense_linear_operator import DenseLinearOperator
 from torch import Tensor
 from torch.nn import ModuleList
 
 
+def get_order(indices: List[int]) -> List[int]:
+    r"""Get the order indices as integers ranging from 0 to the number of indices.
+
+    Args:
+        indices: A list of parameter indices.
+
+    Returns:
+        A list of integers ranging from 0 to the number of indices.
+    """
+    return [i % len(indices) for i in indices]
+
+
+def is_contiguous(indices: List[int]) -> bool:
+    r"""Check if the list of integers is contiguous.
+
+    Args:
+        indices: A list of parameter indices.
+    Returns:
+        A boolean indicating whether the indices are contiguous.
+    """
+    min_idx = min(indices)
+    return set(indices) == set(range(min_idx, min_idx + len(indices)))
+
+
+def get_permutation(decomposition: Dict[str, List[int]]) -> Optional[List[int]]:
+    """Construct permutation to reorder the parameters such that:
+
+    1) the parameters for each context are contiguous.
+    2) The parameters for each context are in the same order
+
+    Args:
+        decomposition: A dictionary mapping context names to a list of
+            parameters.
+    Returns:
+        A permutation to reorder the parameters for (1) and (2).
+        Returning `None` means that ordering specified in `decomposition`
+        satisfies (1) and (2).
+    """
+    permutation = None
+    if not all(
+        is_contiguous(indices=active_parameters)
+        for active_parameters in decomposition.values()
+    ):
+        permutation = _create_new_permutation(decomposition=decomposition)
+    else:
+        same_order = True
+        expected_order = get_order(indices=next(iter(decomposition.values())))
+        for active_parameters in decomposition.values():
+            order = get_order(indices=active_parameters)
+            if order != expected_order:
+                same_order = False
+                break
+        if not same_order:
+            permutation = _create_new_permutation(decomposition=decomposition)
+    return permutation
+
+
+def _create_new_permutation(decomposition: Dict[str, List[int]]) -> List[int]:
+    # make contiguous and ordered
+    permutation = []
+    for active_parameters in decomposition.values():
+        sorted_indices = sorted(active_parameters)
+        permutation.extend(sorted_indices)
+    return permutation
+
+
 class LCEAKernel(Kernel):
     r"""The Latent Context Embedding Additive (LCE-A) Kernel.
 
@@ -40,8 +107,7 @@ def __init__(
         r"""
         Args:
             decomposition: Keys index context names. Values are the indexes of
-                parameters belong to the context. The parameter indexes are in the same
-                order across contexts.
+                parameters belong to the context.
             batch_shape: Batch shape as usual for gpytorch kernels. Model does not
                 support batch training. When batch_shape is non-empty, it is used for
                 loading hyper-parameter values generated from MCMC sampling.
@@ -58,26 +124,25 @@ def __init__(
             context_weight_dict: Known population weights of each context.
         """
         super().__init__(batch_shape=batch_shape)
-        self.decomposition = decomposition
         self.batch_shape = batch_shape
         self.train_embedding = train_embedding
         self._device = device
 
-        num_param = len(next(iter(decomposition.values())))
+        self.num_param = len(next(iter(decomposition.values())))
         self.context_list = list(decomposition.keys())
         self.num_contexts = len(self.context_list)
 
         # get parameter space decomposition
         for active_parameters in decomposition.values():
             # check number of parameters are same in each decomp
-            if len(active_parameters) != num_param:
+            if len(active_parameters) != self.num_param:
                 raise ValueError(
-                    "num of parameters needs to be same across all contexts"
+                    "The number of parameters needs to be same across all contexts."
                 )
-        self._indexers = {
-            context: torch.tensor(active_params, device=self.device)
-            for context, active_params in self.decomposition.items()
-        }
+        # reorder the parameter list based on decomposition such that
+        # parameters for each context are contiguous and in the same order for each
+        # context
+        self.permutation = get_permutation(decomposition=decomposition)
         # get context features and set emb dim
         self.context_cat_feature = None
         self.context_emb_feature = None
@@ -102,7 +167,7 @@ def __init__(
         # base kernel
         self.base_kernel = MaternKernel(
             nu=2.5,
-            ard_num_dims=num_param,
+            ard_num_dims=self.num_param,
             batch_shape=batch_shape,
             lengthscale_prior=GammaPrior(3.0, 6.0),
         )
@@ -303,6 +368,11 @@ def _task_embeddings_batch(self) -> Tensor:
             )
         return embeddings
 
+    def train(self, mode: bool = True) -> None:
+        super().train(mode=mode)
+        if not mode:
+            self.register_buffer("_context_covar", self._eval_context_covar())
+
     def forward(
         self,
         x1: Tensor,
@@ -315,35 +385,42 @@ def forward(
         covariance matrices together
         """
         # context covar matrix
-        context_covar = self._eval_context_covar()
+        if not self.training:
+            context_covar = self._context_covar
+        else:
+            context_covar = self._eval_context_covar()
+        if self.permutation is not None:
+            x1 = x1[..., self.permutation]
+            x2 = x2[..., self.permutation]
         # check input batch size if b x ns x n x d: expand context_covar to
         # b x ns x num_context x num_context
         if x1.dim() > context_covar.dim():
-            context_covar = context_covar.expand(*x1.shape[:1] + context_covar.shape)
-        covars = []
-        # TODO: speed computation of covariance matrix
-        for i in range(self.num_contexts):
-            for j in range(self.num_contexts):
-                context1 = self.context_list[i]
-                context2 = self.context_list[j]
-                active_params1 = self._indexers[context1]
-                active_params2 = self._indexers[context2]
-                covars.append(
-                    (
-                        context_covar.index_select(  # pyre-ignore
-                            -1, torch.tensor([j], device=self.device)
-                        ).index_select(
-                            -2, torch.tensor([i], device=self.device)
-                        )  # b x ns x 1 x 1
-                    )
-                    * self.base_kernel(
-                        x1=x1.index_select(-1, active_params1),
-                        x2=x2.index_select(-1, active_params2),
-                        diag=diag,
-                    )
-                )
+            context_covar = context_covar.expand(
+                x1.shape[:-1] + torch.Size([x2.shape[-2]]) + context_covar.shape
+            )
+        # turn last two dimensions of n x (k*d) into (n*k) x d.
+        x1_exp = x1.reshape(*x1.shape[:-2], -1, self.num_param)
+        x2_exp = x2.reshape(*x2.shape[:-2], -1, self.num_param)
+        # batch shape x n*k x n*k
+        base_covar = self.base_kernel(x1_exp, x2_exp)
+        # batch shape x n x n x k x k
+        view_shape = x1.shape[:-2] + torch.Size(
+            [
+                x1.shape[-2],
+                self.num_contexts,
+                x2.shape[-2],
+                self.num_contexts,
+            ]
+        )
+        base_covar_perm = (
+            base_covar.to_dense()
+            .view(view_shape)
+            .permute(*list(range(x1.ndim - 2)), -4, -2, -3, -1)
+        )
+        # then weight by the context kernel
+        # compute the base kernel on the d parameters
+        einsum_str = "...kk, ...nnkk -> ...n" if diag else "...kk, ...kk -> ..."
+        covar_dense = torch.einsum(einsum_str, context_covar, base_covar_perm)
         if diag:
-            res = sum(covars)
-        else:
-            res = SumLinearOperator(*covars)
-        return res
+            return DiagLinearOperator(covar_dense)
+        return DenseLinearOperator(covar_dense)

test/models/kernels/test_contextual.py

@@ -5,7 +5,13 @@
 # LICENSE file in the root directory of this source tree.
 
 import torch
-from botorch.models.kernels.contextual_lcea import LCEAKernel
+from botorch.models.kernels.contextual_lcea import (
+    get_order,
+    get_permutation,
+    is_contiguous,
+    LCEAKernel,
+)
+
 from botorch.models.kernels.contextual_sac import SACKernel
 from botorch.utils.testing import BotorchTestCase
 from gpytorch.kernels.matern_kernel import MaternKernel
@@ -36,19 +42,20 @@ def test_SACKernel(self):
     def testLCEAKernel(self):
         decomposition = {"1": [0, 3], "2": [1, 2]}
         num_contexts = len(decomposition)
-
         kernel = LCEAKernel(decomposition=decomposition, batch_shape=torch.Size([]))
         # test init
         self.assertListEqual(kernel.context_list, ["1", "2"])
-        self.assertDictEqual(kernel.decomposition, decomposition)
 
         self.assertIsInstance(kernel.base_kernel, MaternKernel)
         self.assertIsInstance(kernel.task_covar_module, MaternKernel)
+        self.assertEqual(kernel.permutation, [0, 3, 1, 2])
 
         # test raise of ValueError
-        with self.assertRaises(ValueError):
+        with self.assertRaisesRegex(
+            ValueError, "The number of parameters needs to be same across all contexts."
+        ):
             LCEAKernel(
-                decomposition={"1": [0, 3], "2": [1]}, batch_shape=torch.Size([])
+                decomposition={"1": [0, 1], "2": [2]}, batch_shape=torch.Size([])
             )
 
         # test set_outputscale_list
@@ -181,3 +188,23 @@ def testLCEAKernel(self):
         self.assertEqual(
             context_covar6.shape, torch.Size([3, num_contexts, num_contexts])
         )
+
+    def test_get_permutation(self):
+        decomp = {"a": [0, 1], "b": [2, 3]}
+        permutation = get_permutation(decomp)
+        self.assertIsNone(permutation)
+        # order mismatch
+        decomp = {"a": [1, 0], "b": [2, 3]}
+        permutation = get_permutation(decomp)
+        self.assertEqual(permutation, [0, 1, 2, 3])
+        # non-contiguous
+        decomp = {"a": [0, 2], "b": [1, 3]}
+        permutation = get_permutation(decomp)
+        self.assertEqual(permutation, [0, 2, 1, 3])
+
+    def test_is_contiguous(self):
+        self.assertFalse(is_contiguous([0, 2]))
+        self.assertTrue(is_contiguous([0, 1]))
+
+    def test_get_order(self):
+        self.assertEqual(get_order([1, 10, 3]), [1, 1, 0])