code: def _optimize_acqf_sequential_q(
      opt_inputs: OptimizeAcqfInputs,
  ) -> Tuple[Tensor, Tensor]:
      """
      Helper function for `optimize_acqf` when sequential=True and q > 1.
  
      For each of `q` times, generate a single candidate greedily, then add it to
      the list of pending points.
      """
      _validate_sequential_inputs(opt_inputs)
      # When using sequential optimization, we allocate the total timeout
      # evenly across the individual acquisition optimizations.
      timeout_sec = (
          opt_inputs.timeout_sec / opt_inputs.q
          if opt_inputs.timeout_sec is not None
          else None
      )
      candidate_list, acq_value_list = [], []
      base_X_pending = opt_inputs.acq_function.X_pending
  
      new_inputs = dataclasses.replace(
          opt_inputs,
          q=1,
          batch_initial_conditions=None,
          return_best_only=True,
          sequential=False,
          timeout_sec=timeout_sec,
      )
      for i in range(opt_inputs.q):
          candidate, acq_value = _optimize_acqf_batch(new_inputs)
  
          candidate_list.append(candidate)
          acq_value_list.append(acq_value)
          candidates = torch.cat(candidate_list, dim=-2)
          new_inputs.acq_function.set_X_pending(
              torch.cat([base_X_pending, candidates], dim=-2)
              if base_X_pending is not None
              else candidates
          )
          logger.info(
              f"Generated sequential candidate {i+1} of {opt_inputs.q}"
          )
      opt_inputs.acq_function.set_X_pending(base_X_pending)
      return candidates, torch.stack(acq_value_list)
  
imports: from __future__ import annotations
  import dataclasses
  import warnings
  from typing import Any, Callable, Dict, List, Optional, Tuple, Union
  import torch
  from botorch.acquisition.acquisition import AcquisitionFunction, OneShotAcquisitionFunction
  from botorch.acquisition.knowledge_gradient import qKnowledgeGradient
  from botorch.acquisition.multi_objective.hypervolume_knowledge_gradient import qHypervolumeKnowledgeGradient
  from botorch.exceptions import InputDataError, UnsupportedError
  from botorch.exceptions.warnings import OptimizationWarning
  from botorch.generation.gen import gen_candidates_scipy, TGenCandidates
  from botorch.logging import logger
  from botorch.optim.initializers import gen_batch_initial_conditions, gen_one_shot_hvkg_initial_conditions, gen_one_shot_kg_initial_conditions, TGenInitialConditions
  from botorch.optim.stopping import ExpMAStoppingCriterion
  from botorch.optim.utils import _filter_kwargs
  from torch import Tensor
label_desc: Use image node_id 4 for calling a global function with example usage: _optimize_acqf_sequential_q(opt_inputs) and returns: candidates,  torch