code: def gen_value_function_initial_conditions(
      acq_function: AcquisitionFunction,
      bounds: Tensor,
      num_restarts: int,
      raw_samples: int,
      current_model: Model,
      fixed_features: Optional[Dict[int, float]] = None,
      options: Optional[Dict[str, Union[bool, float, int]]] = None,
  ) -> Tensor:
      r"""Generate a batch of smart initializations for optimizing
      the value function of qKnowledgeGradient.
  
      This function generates initial conditions for optimizing the inner problem of
      KG, i.e. its value function, using the maximizer of the posterior objective.
      Intutively, the maximizer of the fantasized posterior will often be close to a
      maximizer of the current posterior. This function uses that fact to generate the
      initital conditions for the fantasy points. Specifically, a fraction of `1 -
      frac_random` (see options) of raw samples is generated by sampling from the set of
      maximizers of the posterior objective (obtained via random restart optimization)
      according to a softmax transformation of their respective values. This means that
      this initialization strategy internally solves an acquisition function
      maximization problem. The remaining raw samples are generated using
      `draw_sobol_samples`. All raw samples are then evaluated, and the initial
      conditions are selected according to the standard initialization strategy in
      'initialize_q_batch' individually for each inner problem.
  
      Args:
          acq_function: The value function instance to be optimized.
          bounds: A `2 x d` tensor of lower and upper bounds for each column of
              task features.
          num_restarts: The number of starting points for multistart acquisition
              function optimization.
          raw_samples: The number of raw samples to consider in the initialization
              heuristic.
          current_model: The model of the KG acquisition function that was used to
              generate the fantasy model of the value function.
          fixed_features: A map `{feature_index: value}` for features that
              should be fixed to a particular value during generation.
          options: Options for initial condition generation. These contain all
              settings for the standard heuristic initialization from
              `gen_batch_initial_conditions`. In addition, they contain
              `frac_random` (the fraction of fully random fantasy points),
              `num_inner_restarts` and `raw_inner_samples` (the number of random
              restarts and raw samples for solving the posterior objective
              maximization problem, respectively) and `eta` (temperature parameter
              for sampling heuristic from posterior objective maximizers).
  
      Returns:
          A `num_restarts x batch_shape x q x d` tensor that can be used as initial
          conditions for `optimize_acqf()`. Here `batch_shape` is the batch shape
          of value function model.
  
      Example:
          >>> fant_X = torch.rand(5, 1, 2)
          >>> fantasy_model = model.fantasize(fant_X, SobolQMCNormalSampler(16))
          >>> value_function = PosteriorMean(fantasy_model)
          >>> bounds = torch.tensor([[0., 0.], [1., 1.]])
          >>> Xinit = gen_value_function_initial_conditions(
          >>>     value_function, bounds, num_restarts=10, raw_samples=512,
          >>>     options={"frac_random": 0.25},
          >>> )
      """
      options = options or {}
      seed: Optional[int] = options.get("seed")
      frac_random: float = options.get("frac_random", 0.6)
      if not 0 < frac_random < 1:
          raise ValueError(
              f"frac_random must take on values in (0,1). Value: {frac_random}"
          )
  
      # compute maximizer of the current value function
      value_function = _get_value_function(
          model=current_model,
          objective=getattr(acq_function, "objective", None),
          posterior_transform=acq_function.posterior_transform,
          sampler=getattr(acq_function, "sampler", None),
          project=getattr(acq_function, "project", None),
      )
      from botorch.optim.optimize import optimize_acqf
  
      fantasy_cands, fantasy_vals = optimize_acqf(
          acq_function=value_function,
          bounds=bounds,
          q=1,
          num_restarts=options.get("num_inner_restarts", 20),
          raw_samples=options.get("raw_inner_samples", 1024),
          fixed_features=fixed_features,
          return_best_only=False,
          options={
              k: v
              for k, v in options.items()
              if k
              not in (
                  "frac_random",
                  "num_inner_restarts",
                  "raw_inner_samples",
                  "eta",
              )
          },
      )
  
      batch_shape = acq_function.model.batch_shape
      # sampling from the optimizers
      n_value = int(
          (1 - frac_random) * raw_samples
      )  # number of non-random ICs
      if n_value > 0:
          eta = options.get("eta", 2.0)
          weights = torch.exp(eta * standardize(fantasy_vals))
          idx = batched_multinomial(
              weights=weights.expand(*batch_shape, -1),
              num_samples=n_value,
              replacement=True,
          ).permute(-1, *range(len(batch_shape)))
          resampled = fantasy_cands[idx]
      else:
          resampled = torch.empty(
              0,
              *batch_shape,
              1,
              bounds.shape[-1],
              dtype=fantasy_cands.dtype,
              device=fantasy_cands.device,
          )
      # add qMC samples
      randomized = draw_sobol_samples(
          bounds=bounds,
          n=raw_samples - n_value,
          q=1,
          batch_shape=batch_shape,
          seed=seed,
      ).to(resampled)
      # full set of raw samples
      X_rnd = torch.cat([resampled, randomized], dim=0)
      X_rnd = fix_features(X_rnd, fixed_features=fixed_features)
  
      # evaluate the raw samples
      with torch.no_grad():
          Y_rnd = acq_function(X_rnd)
  
      # select the restart points using the heuristic
      return initialize_q_batch(
          X=X_rnd, Y=Y_rnd, n=num_restarts, eta=options.get("eta", 2.0)
      )
  
imports: from __future__ import annotations
  import warnings
  from math import ceil
  from typing import Callable, Dict, List, Optional, Tuple, Union
  import torch
  from botorch import settings
  from botorch.acquisition import analytic, monte_carlo, multi_objective
  from botorch.acquisition.acquisition import AcquisitionFunction
  from botorch.acquisition.fixed_feature import FixedFeatureAcquisitionFunction
  from botorch.acquisition.knowledge_gradient import _get_value_function, qKnowledgeGradient
  from botorch.acquisition.multi_objective.hypervolume_knowledge_gradient import _get_hv_value_function, qHypervolumeKnowledgeGradient, qMultiFidelityHypervolumeKnowledgeGradient
  from botorch.exceptions.errors import BotorchTensorDimensionError, UnsupportedError
  from botorch.exceptions.warnings import BadInitialCandidatesWarning, BotorchWarning, SamplingWarning
  from botorch.models.model import Model
  from botorch.optim.utils import fix_features, get_X_baseline
  from botorch.utils.multi_objective.pareto import is_non_dominated
  from botorch.utils.sampling import batched_multinomial, draw_sobol_samples, get_polytope_samples, manual_seed
  from botorch.utils.transforms import normalize, standardize, unnormalize
  from torch import Tensor
  from torch.distributions import Normal
  from torch.quasirandom import SobolEngine
label_desc: Use image node_id 8 for calling a global function with example usage: gen_value_function_initial_conditions(acq_function, bounds, num_restarts, raw_samples, current_model, fixed_features, options) and returns: initialize_q_batch