code: def _get_customized_covar_module(
      covar_module_prior_dict: Dict[str, Prior],
      ard_num_dims: int,
      aug_batch_shape: torch.Size,
      task_feature: Optional[int] = None,
  ) -> Kernel:
      """Construct a GP kernel based on customized prior dict.
  
      Args:
          covar_module_prior_dict: Dict. The keys are the names of the prior and values
              are the priors. e.g. {"lengthscale_prior": GammaPrior(3.0, 6.0)}.
          ard_num_dims: The dimension of the inputs, including task features.
          aug_batch_shape: The output dimension augmented batch shape of the model
              (different from the batch shape for batched multi-output models).
          task_feature: The index of the task feature.
      """
      # TODO: add more checks of covar_module_prior_dict
      if task_feature is not None:
          ard_num_dims -= 1
      return ScaleKernel(
          MaternKernel(
              nu=2.5,
              ard_num_dims=ard_num_dims,
              batch_shape=aug_batch_shape,
              lengthscale_prior=covar_module_prior_dict.get(
                  "lengthscale_prior", GammaPrior(3.0, 6.0)
              ),
          ),
          batch_shape=aug_batch_shape,
          outputscale_prior=covar_module_prior_dict.get(
              "outputscale_prior", GammaPrior(2.0, 0.15)
          ),
      )
  
imports: import functools
  from copy import deepcopy
  from random import randint
  from typing import Any, Callable, Dict, List, Optional, Protocol, Tuple, Type, Union
  import torch
  from ax.models.model_utils import best_observed_point, get_observed
  from ax.models.torch.utils import _to_inequality_constraints
  from ax.models.torch_base import TorchModel
  from ax.models.types import TConfig
  from botorch.acquisition import get_acquisition_function
  from botorch.acquisition.acquisition import AcquisitionFunction
  from botorch.acquisition.fixed_feature import FixedFeatureAcquisitionFunction
  from botorch.acquisition.objective import ConstrainedMCObjective, GenericMCObjective
  from botorch.acquisition.utils import get_infeasible_cost
  from botorch.exceptions.errors import UnsupportedError
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.gp_regression_fidelity import SingleTaskMultiFidelityGP
  from botorch.models.gpytorch import GPyTorchModel
  from botorch.models.model import Model
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.multitask import MultiTaskGP
  from botorch.models.transforms.input import Warp
  from botorch.optim.optimize import optimize_acqf
  from botorch.utils import get_objective_weights_transform, get_outcome_constraint_transforms
  from botorch.utils.multi_objective.scalarization import get_chebyshev_scalarization
  from botorch.utils.transforms import is_ensemble
  from gpytorch.kernels import MaternKernel, ScaleKernel
  from gpytorch.kernels.kernel import Kernel
  from gpytorch.mlls.exact_marginal_log_likelihood import ExactMarginalLogLikelihood
  from gpytorch.mlls.leave_one_out_pseudo_likelihood import LeaveOneOutPseudoLikelihood
  from gpytorch.mlls.sum_marginal_log_likelihood import SumMarginalLogLikelihood
  from gpytorch.priors import Prior
  from gpytorch.priors.lkj_prior import LKJCovariancePrior
  from gpytorch.priors.torch_priors import GammaPrior, LogNormalPrior
  from torch import Tensor
label_desc: Use image node_id 13 for calling a global function with example usage: _get_customized_covar_module(covar_module_prior_dict, ard_num_dims, aug_batch_shape, task_feature) and returns: ScaleKernel