code: def cost_fn(X):
      costs = torch.ones(
          X.shape[:-1] + torch.Size([2]), dtype=X.dtype, device=X.device
      )
      costs[..., 1] = 3.0
      return costs
  
imports: from itertools import product
  from unittest import mock
  import numpy
  import torch
  from botorch.acquisition.cost_aware import InverseCostWeightedUtility
  from botorch.acquisition.multi_objective.hypervolume_knowledge_gradient import _get_hv_value_function, _split_hvkg_fantasy_points, qHypervolumeKnowledgeGradient, qMultiFidelityHypervolumeKnowledgeGradient
  from botorch.acquisition.multi_objective.objective import GenericMCMultiOutputObjective, IdentityMCMultiOutputObjective
  from botorch.exceptions.errors import UnsupportedError
  from botorch.models.deterministic import GenericDeterministicModel
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.sampling.list_sampler import ListSampler
  from botorch.sampling.normal import SobolQMCNormalSampler
  from botorch.utils.multi_objective.box_decompositions.dominated import DominatedPartitioning
  from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
label_desc: Use image node_id 1 for calling a global function with example usage: cost_fn(X) and returns: costs