code: def warmstart_multistep(
      acq_function: qMultiStepLookahead,
      bounds: Tensor,
      num_restarts: int,
      raw_samples: int,
      full_optimizer: Tensor,
      **kwargs: Any,
  ) -> Tensor:
      r"""Warm-start initialization for multi-step look-ahead acquisition functions.
  
      For now uses the same q' as in `full_optimizer`. TODO: allow different `q`.
  
      Args:
          acq_function: A qMultiStepLookahead acquisition function.
          bounds: A `2 x d` tensor of lower and upper bounds for each column of 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.
          full_optimizer: The full tree of optimizers of the previous iteration of shape
              `batch_shape x q' x d`. Typically obtained by passing
              `return_best_only=False` and `return_full_tree=True` into `optimize_acqf`.
          kwargs: Optimization kwargs.
  
      Returns:
          A `num_restarts x q' x d` tensor for initial points for optimization.
  
      This is a very simple initialization heuristic.
      TODO: Use the observed values to identify the fantasy sub-tree that is closest to
      the observed value.
      """
      batch_shape, shapes, sizes = acq_function.get_split_shapes(
          full_optimizer
      )
      Xopts = torch.split(full_optimizer, sizes, dim=-2)
      tkwargs = {"device": Xopts[0].device, "dtype": Xopts[0].dtype}
  
      B = Beta(torch.ones(1, **tkwargs), 3 * torch.ones(1, **tkwargs))
  
      def mixin_layer(X: Tensor, bounds: Tensor, eta: float) -> Tensor:
          perturbations = unnormalize(
              B.sample(X.shape).squeeze(-1), bounds
          )
          return (1 - eta) * X + eta * perturbations
  
      def make_init_tree(
          Xopts: List[Tensor], bounds: Tensor, etas: Tensor
      ) -> Tensor:
          Xtrs = [
              mixin_layer(X=X, bounds=bounds, eta=eta)
              for eta, X in zip(etas, Xopts)
          ]
          return torch.cat(Xtrs, dim=-2)
  
      def mixin_tree(T: Tensor, bounds: Tensor, alpha: float) -> Tensor:
          return (1 - alpha) * T + alpha * unnormalize(
              torch.rand_like(T), bounds
          )
  
      n_repeat = math.ceil(raw_samples / batch_shape[0])
      alphas = torch.linspace(0, 0.75, n_repeat, **tkwargs)
      etas = torch.linspace(0.1, 1.0, len(Xopts), **tkwargs)
  
      X_full = torch.cat(
          [
              mixin_tree(
                  T=make_init_tree(
                      Xopts=Xopts, bounds=bounds, etas=etas
                  ),
                  bounds=bounds,
                  alpha=alpha,
              )
              for alpha in alphas
          ],
          dim=0,
      )
  
      with torch.no_grad():
          Y_full = acq_function(X_full)
      X_init = initialize_q_batch(
          X=X_full, Y=Y_full, n=num_restarts, eta=1.0
      )
      return X_init[:raw_samples]
  
imports: from __future__ import annotations
  import math
  import warnings
  from typing import Any, Callable, Dict, List, Optional, Tuple, Type
  import numpy
  import torch
  from botorch.acquisition import AcquisitionFunction, OneShotAcquisitionFunction
  from botorch.acquisition.analytic import AnalyticAcquisitionFunction, PosteriorMean
  from botorch.acquisition.monte_carlo import MCAcquisitionFunction
  from botorch.acquisition.objective import MCAcquisitionObjective, PosteriorTransform
  from botorch.exceptions.errors import UnsupportedError
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models.model import Model
  from botorch.optim.initializers import initialize_q_batch
  from botorch.sampling.base import MCSampler
  from botorch.sampling.normal import SobolQMCNormalSampler
  from botorch.utils.transforms import match_batch_shape, t_batch_mode_transform, unnormalize
  from torch import Size, Tensor
  from torch.distributions import Beta
  from torch.nn import ModuleList
label_desc: Use image node_id 6 for calling a global function with example usage: warmstart_multistep(acq_function, bounds, num_restarts, raw_samples, full_optimizer) and returns: X_init, unknown, torch, unknown