code: def test_learned_preference_objective(self) -> None:
      seed = torch.randint(low=0, high=10, size=torch.Size([1]))
      torch.manual_seed(seed)
      pref_model = self._get_pref_model(dtype=torch.float64)
  
      og_sample_shape = 3
      large_sample_shape = 256
      batch_size = 2
      q = 8
      test_X = torch.rand(
          torch.Size((og_sample_shape, batch_size, q, self.x_dim)),
          dtype=torch.float64,
      )
      large_X = torch.rand(
          torch.Size((large_sample_shape, batch_size, q, self.x_dim)),
          dtype=torch.float64,
      )
  
      # test default setting where sampler =
      # IIDNormalSampler(sample_shape=torch.Size([1]))
      with self.subTest("default sampler"):
          pref_obj = LearnedObjective(pref_model=pref_model)
          first_call_output = pref_obj(test_X)
          self.assertEqual(
              first_call_output.shape,
              torch.Size(
                  [
                      og_sample_shape * DEFAULT_NUM_PREF_SAMPLES,
                      batch_size,
                      q,
                  ]
              ),
          )
          # Making sure the sampler has correct base_samples shape
          self.assertEqual(
              pref_obj.sampler.base_samples.shape,
              torch.Size(
                  [DEFAULT_NUM_PREF_SAMPLES, og_sample_shape, 1, q]
              ),
          )
          # Passing through a same-shaped X again shouldn't change the base sample
          previous_base_samples = pref_obj.sampler.base_samples
          another_test_X = torch.rand_like(test_X)
          pref_obj(another_test_X)
          self.assertIs(
              pref_obj.sampler.base_samples, previous_base_samples
          )
  
          with self.assertRaisesRegex(
              ValueError, "samples should have at least 3 dimensions."
          ):
              pref_obj(torch.rand(q, self.x_dim, dtype=torch.float64))
  
      # test when sampler has multiple preference samples
      with self.subTest("Multiple samples"):
          num_samples = 256
          pref_obj = LearnedObjective(
              pref_model=pref_model,
              sample_shape=torch.Size([num_samples]),
          )
          self.assertEqual(
              pref_obj(test_X).shape,
              torch.Size(
                  [num_samples * og_sample_shape, batch_size, q]
              ),
          )
  
          avg_obj_val = pref_obj(large_X).mean(dim=0)
          flipped_avg_obj_val = pref_obj(large_X.flip(dims=[0])).mean(
              dim=0
          )
          # Check if they are approximately close.
          # The variance is large hence the loose atol.
          self.assertAllClose(
              avg_obj_val, flipped_avg_obj_val, atol=1e-2
          )
  
      # test posterior mean
      with self.subTest("PosteriorMeanModel"):
          mean_pref_model = PosteriorMeanModel(model=pref_model)
          pref_obj = LearnedObjective(pref_model=mean_pref_model)
          self.assertEqual(
              pref_obj(test_X).shape,
              torch.Size([og_sample_shape, batch_size, q]),
          )
  
          # the order of samples shouldn't matter
          avg_obj_val = pref_obj(large_X).mean(dim=0)
          flipped_avg_obj_val = pref_obj(large_X.flip(dims=[0])).mean(
              dim=0
          )
          # When we use the posterior mean objective, they should be very close
          self.assertAllClose(avg_obj_val, flipped_avg_obj_val)
  
      # cannot use a deterministic model together with a sampler
      with self.subTest("deterministic model"), self.assertRaises(
          AssertionError
      ):
          LearnedObjective(
              pref_model=mean_pref_model,
              sample_shape=torch.Size([num_samples]),
          )
  
imports: import itertools
  import warnings
  from typing import Optional
  import torch
  from botorch import settings
  from botorch.acquisition import LearnedObjective
  from botorch.acquisition.objective import ConstrainedMCObjective, DEFAULT_NUM_PREF_SAMPLES, ExpectationPosteriorTransform, GenericMCObjective, IdentityMCObjective, LEARNED_OBJECTIVE_PREF_MODEL_MIXED_DTYPE_WARN, LinearMCObjective, MCAcquisitionObjective, PosteriorTransform, ScalarizedPosteriorTransform
  from botorch.exceptions.errors import UnsupportedError
  from botorch.exceptions.warnings import _get_single_precision_warning, InputDataWarning
  from botorch.models.deterministic import PosteriorMeanModel
  from botorch.models.pairwise_gp import PairwiseGP
  from botorch.models.transforms.input import Normalize
  from botorch.posteriors import GPyTorchPosterior
  from botorch.utils import apply_constraints
  from botorch.utils.testing import _get_test_posterior, BotorchTestCase
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from linear_operator.operators.dense_linear_operator import to_linear_operator
  from torch import Tensor
label_desc: Use image node_id 3 for calling the TestLearnedObjective obj's underlying member method code with example usage: obj.test_learned_preference_objective() without return types