botorch/acquisition/max_value_entropy_search.py [298:324]:
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    r"""The acquisition function for Max-value Entropy Search.

    This acquisition function computes the mutual information of max values and
    a candidate point X. See [Wang2017mves]_ for a detailed discussion.

    The model must be single-outcome. The batch case `q > 1` is supported
    through cyclic optimization and fantasies.

    Example:
        >>> model = SingleTaskGP(train_X, train_Y)
        >>> candidate_set = torch.rand(1000, bounds.size(1))
        >>> candidate_set = bounds[0] + (bounds[1] - bounds[0]) * candidate_set
        >>> MES = qMaxValueEntropy(model, candidate_set)
        >>> mes = MES(test_X)
    """

    def __init__(
        self,
        model: Model,
        candidate_set: Tensor,
        num_fantasies: int = 16,
        num_mv_samples: int = 10,
        num_y_samples: int = 128,
        posterior_transform: Optional[PosteriorTransform] = None,
        use_gumbel: bool = True,
        maximize: bool = True,
        X_pending: Optional[Tensor] = None,
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botorch/acquisition/max_value_entropy_search.py [650:678]:
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    r"""Multi-fidelity max-value entropy.

    The acquisition function for multi-fidelity max-value entropy search
    with support for trace observations. See [Takeno2020mfmves]_
    for a detailed discussion of the basic ideas on multi-fidelity MES
    (note that this implementation is somewhat different).

    The model must be single-outcome, unless using a PosteriorTransform.
    The batch case `q > 1` is supported through cyclic optimization and fantasies.

    Example:
        >>> model = SingleTaskGP(train_X, train_Y)
        >>> candidate_set = torch.rand(1000, bounds.size(1))
        >>> candidate_set = bounds[0] + (bounds[1] - bounds[0]) * candidate_set
        >>> MF_MES = qMultiFidelityMaxValueEntropy(model, candidate_set)
        >>> mf_mes = MF_MES(test_X)
    """

    def __init__(
        self,
        model: Model,
        candidate_set: Tensor,
        num_fantasies: int = 16,
        num_mv_samples: int = 10,
        num_y_samples: int = 128,
        posterior_transform: Optional[PosteriorTransform] = None,
        use_gumbel: bool = True,
        maximize: bool = True,
        X_pending: Optional[Tensor] = None,
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