botorch/acquisition/monte_carlo.py [133:158]:
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    ) -> None:
        r"""q-Expected Improvement.

        Args:
            model: A fitted model.
            best_f: The best objective value observed so far (assumed noiseless). Can be
                a `batch_shape`-shaped tensor, which in case of a batched model
                specifies potentially different values for each element of the batch.
            sampler: The sampler used to draw base samples. Defaults to
                `SobolQMCNormalSampler(num_samples=512, collapse_batch_dims=True)`
            objective: The MCAcquisitionObjective under which the samples are evaluated.
                Defaults to `IdentityMCObjective()`.
            posterior_transform: A PosteriorTransform (optional).
            X_pending:  A `m x d`-dim Tensor of `m` design points that have been
                submitted for function evaluation but have not yet been evaluated.
                Concatenated into X upon forward call. Copied and set to have no
                gradient.
        """
        super().__init__(
            model=model,
            sampler=sampler,
            objective=objective,
            posterior_transform=posterior_transform,
            X_pending=X_pending,
        )
        self.register_buffer("best_f", torch.as_tensor(best_f, dtype=float))
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botorch/acquisition/monte_carlo.py [412:441]:
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    ) -> None:
        r"""q-Probability of Improvement.

        Args:
            model: A fitted model.
            best_f: The best objective value observed so far (assumed noiseless). Can
                be a `batch_shape`-shaped tensor, which in case of a batched model
                specifies potentially different values for each element of the batch.
            sampler: The sampler used to draw base samples. Defaults to
                `SobolQMCNormalSampler(num_samples=512, collapse_batch_dims=True)`
            objective: The MCAcquisitionObjective under which the samples are
                evaluated. Defaults to `IdentityMCObjective()`.
            posterior_transform: A PosteriorTransform (optional).
            X_pending:  A `m x d`-dim Tensor of `m` design points that have
                points that have been submitted for function evaluation
                but have not yet been evaluated.  Concatenated into X upon
                forward call.  Copied and set to have no gradient.
            tau: The temperature parameter used in the sigmoid approximation
                of the step function. Smaller values yield more accurate
                approximations of the function, but result in gradients
                estimates with higher variance.
        """
        super().__init__(
            model=model,
            sampler=sampler,
            objective=objective,
            posterior_transform=posterior_transform,
            X_pending=X_pending,
        )
        self.register_buffer("best_f", torch.as_tensor(best_f, dtype=float))
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