Bayesian Exploration Generator¶

`BayesianExplorationGenerator` ¶

Bases: BayesianGenerator

Bayesian exploration generator for autonomous characterization.

Source code in xopt/generators/bayesian/bayesian_exploration.py

class BayesianExplorationGenerator(BayesianGenerator):
    """
    Bayesian exploration generator for autonomous characterization.
    """

    name = "bayesian_exploration"
    supports_batch_generation: bool = True
    supports_constraints: bool = True
    supports_multi_objective: bool = True
    supports_single_objective: bool = True

    __doc__ = "Bayesian exploration generator\n" + formatted_base_docstring()

    _compatible_turbo_controllers = [SafetyTurboController]

    @field_validator("vocs", mode="after")
    def validate_vocs(cls, v, info):
        # start by using the superclass validator
        v = super().validate_vocs(v, info)

        # assert that all of the objectives are of type "ExploreObjective"
        for obj in v.objectives.values():
            if not isinstance(obj, ExploreObjective):
                raise VOCSError(
                    "BayesianExplorationGenerator only supports ExploreObjective objectives"
                )
        return v

    def _get_acquisition(self, model: Model) -> MCAcquisitionFunction:
        """
        Get the acquisition function for Bayesian Optimization.

        Parameters
        ----------
        model : Model
            The model used for Bayesian Optimization.

        Returns
        -------
        MCAcquisitionFunction
            The acquisition function for Bayesian Optimization.
        """
        sampler = self._get_sampler(model)
        qPV = qPosteriorVariance(
            model,
            sampler=sampler,
            objective=self._get_objective(),
        )

        return qPV

`model_input_names` `property` ¶

variable names corresponding to trained model

`init(**kwargs)` ¶

Initialize the generator.

Source code in xopt/generator.py

def __init__(self, **kwargs):
    """
    Initialize the generator.
    """
    super().__init__(**kwargs)
    logger.info(f"Initialized generator {self.name}")

`add_data(new_data)` ¶

Add new data to the generator for Bayesian Optimization.

Parameters:

Name	Type	Description	Default
`new_data`	`DataFrame`	The new data to be added to the generator.	required

Notes

This method appends the new data to the existing data in the generator.

Source code in xopt/generators/bayesian/bayesian_generator.py

def add_data(self, new_data: pd.DataFrame):
    """
    Add new data to the generator for Bayesian Optimization.

    Parameters
    ----------
    new_data : pd.DataFrame
        The new data to be added to the generator.

    Notes
    -----
    This method appends the new data to the existing data in the generator.
    """
    self.data = pd.concat([self.data, new_data], axis=0, ignore_index=True)

`generate(n_candidates)` ¶

Generate candidates using Bayesian Optimization.

Parameters:

Name	Type	Description	Default
`n_candidates`	`int`	The number of candidates to generate in each optimization step.	required

Returns:

Type	Description
`List[Dict]`	A list of dictionaries containing the generated candidates.

Raises:

Type	Description
`NotImplementedError`	If the number of candidates is greater than 1, and the generator does not support batch candidate generation.
`RuntimeError`	If no data is contained in the generator, the 'add_data' method should be called to add data before generating candidates.

Notes

This method generates candidates for Bayesian Optimization based on the provided number of candidates. It updates the internal model with the current data and calculates the candidates by optimizing the acquisition function. The method returns the generated candidates in the form of a list of dictionaries.

Source code in xopt/generators/bayesian/bayesian_generator.py

def generate(self, n_candidates: int):
    """
    Generate candidates using Bayesian Optimization.

    Parameters
    ----------
    n_candidates : int
        The number of candidates to generate in each optimization step.

    Returns
    -------
    List[Dict]
        A list of dictionaries containing the generated candidates.

    Raises
    ------
    NotImplementedError
        If the number of candidates is greater than 1, and the generator does not
        support batch candidate generation.

    RuntimeError
        If no data is contained in the generator, the 'add_data' method should be
        called to add data before generating candidates.

    Notes
    -----
    This method generates candidates for Bayesian Optimization based on the
    provided number of candidates. It updates the internal model with the current
    data and calculates the candidates by optimizing the acquisition function.
    The method returns the generated candidates in the form of a list of dictionaries.
    """

    self.n_candidates = n_candidates
    if n_candidates > 1 and not self.supports_batch_generation:
        raise NotImplementedError(
            "This Bayesian algorithm does not currently support parallel candidate "
            "generation"
        )

    # if no data exists raise error
    if self.data is None:
        raise RuntimeError(
            "no data contained in generator, call `add_data` "
            "method to add data, see also `Xopt.random_evaluate()`"
        )

    else:
        # dict to track runtimes
        timing_results = {}

        # update internal model with internal data
        start_time = time.perf_counter()
        model = self.train_model(self.get_training_data(self.data))
        timing_results["training"] = time.perf_counter() - start_time

        # propose candidates given model
        start_time = time.perf_counter()
        candidates = self.propose_candidates(model, n_candidates=n_candidates)
        timing_results["acquisition_optimization"] = (
            time.perf_counter() - start_time
        )

        # post process candidates
        result = self._process_candidates(candidates)

        # append timing results to dataframe (if it exists)
        if self.computation_time is not None:
            self.computation_time = pd.concat(
                (
                    self.computation_time,
                    pd.DataFrame(timing_results, index=[0]),
                ),
                ignore_index=True,
            )
        else:
            self.computation_time = pd.DataFrame(timing_results, index=[0])

        if self.n_interpolate_points is not None:
            if self.n_candidates > 1:
                raise RuntimeError(
                    "cannot generate interpolated points for "
                    "multiple candidate generation"
                )
            else:
                assert len(result) == 1
                result = interpolate_points(
                    pd.concat(
                        (self.data.iloc[-1:][self.vocs.variable_names], result),
                        axis=0,
                        ignore_index=True,
                    ),
                    num_points=self.n_interpolate_points,
                )

        return result.to_dict("records")

`get_acquisition(model)` ¶

Define the acquisition function based on the given GP model.

Lives on target device specified by tkwargs / use_cuda.

Parameters:

Name	Type	Description	Default
`model`	`Module`	The BoTorch model to be used for generating the acquisition function.	required

Returns:

Name	Type	Description
`acqusition_function`	`AcquisitionFunction`

Raises:

Type	Description
`ValueError`	If the provided 'model' is None. A valid model is required to create the acquisition function.

Source code in xopt/generators/bayesian/bayesian_generator.py

def get_acquisition(self, model: Module) -> AcquisitionFunction:
    """
    Define the acquisition function based on the given GP model.

    Lives on target device specified by tkwargs / use_cuda.

    Parameters
    ----------
    model : Module
        The BoTorch model to be used for generating the acquisition function.

    Returns
    -------
    acqusition_function : AcquisitionFunction

    Raises
    ------
    ValueError
        If the provided 'model' is None. A valid model is required to create the
        acquisition function.
    """
    if model is None:
        raise ValueError("model cannot be None")

    # get base acquisition function
    acq = self._get_acquisition(model)

    # apply constraints if specified in vocs
    # TODO: replace with direct constrainted acquisition function calls
    # see SampleReducingMCAcquisitionFunction in botorch for rationale
    if len(self.vocs.constraints):
        try:
            sampler = acq.sampler
        except AttributeError:
            sampler = self._get_sampler(model)

        acq = ConstrainedMCAcquisitionFunction(
            model, acq, self._get_constraint_callables(), sampler=sampler
        )

        # log transform the result to handle the constraints
        acq = LogAcquisitionFunction(acq)

    acq = self._apply_fixed_features(acq)
    acq = acq.to(**self.tkwargs)
    return acq

`get_input_data(data)` ¶

Convert input data to a torch tensor.

Parameters:

Name	Type	Description	Default
`data`	`DataFrame`	The input data in the form of a pandas DataFrame.	required

Returns:

Type	Description
`Tensor`	A torch tensor containing the input data.

Notes

This method takes a pandas DataFrame as input data and converts it into a torch tensor. It specifically selects columns corresponding to the model's input names (variables), and the resulting tensor is configured with the data type and device settings from the generator.

Source code in xopt/generators/bayesian/bayesian_generator.py

def get_input_data(self, data: pd.DataFrame) -> torch.Tensor:
    """
    Convert input data to a torch tensor.

    Parameters
    ----------
    data : pd.DataFrame
        The input data in the form of a pandas DataFrame.

    Returns
    -------
    torch.Tensor
        A torch tensor containing the input data.

    Notes
    -----
    This method takes a pandas DataFrame as input data and converts it into a
    torch tensor. It specifically selects columns corresponding to the model's
    input names (variables), and the resulting tensor is configured with the data
    type and device settings from the generator.
    """
    return torch.tensor(
        data[self.model_input_names].to_numpy().copy(), **self.tkwargs
    )

`get_optimum()` ¶

select the best point(s) given by the model using the Posterior mean

Source code in xopt/generators/bayesian/bayesian_generator.py

def get_optimum(self):
    """select the best point(s) given by the
    model using the Posterior mean"""
    acq = qUpperConfidenceBound(
        model=self.model, beta=0.0, objective=self._get_objective()
    )
    if len(self.vocs.constraints):
        acq = ConstrainedMCAcquisitionFunction(
            self.model,
            acq,
            self._get_constraint_callables(),
            sampler=self._get_sampler(self.model),
        )
    bounds = self._get_bounds()

    if self.fixed_features is not None:
        acq = self._apply_fixed_features(acq)

        indices = []
        for idx, name in enumerate(self.vocs.variable_names):
            if name not in self.fixed_features:
                indices += [idx]

        bounds = bounds[:, indices]

    bounds = bounds.to(**self.tkwargs)
    acq = acq.to(**self.tkwargs)

    # use default initial conditions for a global search
    result = self.numerical_optimizer.optimize(acq, bounds, 1)

    return self._process_candidates(result)

`get_training_data(data)` ¶

Get training data used to train the GP model.

If a turbo controller is specified with the flag restrict_model_data this will return a subset of data that is inside the trust region.

Parameters:

Name	Type	Description	Default
`data`	`DataFrame`	The data in the form of a pandas DataFrame.	required

Returns:

Name	Type	Description
`data`	`DataFrame`	A subset of data used to train the model form of a pandas DataFrame.

Source code in xopt/generators/bayesian/bayesian_generator.py

def get_training_data(self, data: pd.DataFrame) -> pd.DataFrame:
    """
    Get training data used to train the GP model.

    If a turbo controller is specified with the flag `restrict_model_data` this
    will return a subset of data that is inside the trust region.

    Parameters
    ----------
    data : pd.DataFrame
        The data in the form of a pandas DataFrame.

    Returns
    -------
    data : pd.DataFrame
        A subset of data used to train the model form of a pandas DataFrame.

    """
    if self.turbo_controller is not None:
        if self.turbo_controller.restrict_model_data:
            data = self.turbo_controller.get_data_in_trust_region(data, self)
            if data.empty:
                raise FeasibilityError(
                    "No training data available to build model, because ",
                    "no points in the dataset are within the TuRBO trust region. ",
                )
    return data

`model_dump(*args, **kwargs)` ¶

overwrite model dump to remove faux class attrs

Source code in xopt/generator.py

def model_dump(self, *args: Any, **kwargs: Any) -> dict[str, Any]:
    """overwrite model dump to remove faux class attrs"""

    res = super().model_dump(*args, **kwargs)

    res.pop("supports_batch_generation", None)
    res.pop("supports_multi_objective", None)

    return res

`propose_candidates(model, n_candidates=1)` ¶

Propose candidates using Bayesian Optimization.

Parameters:

Name	Type	Description	Default
`model`	`Module`	The trained Bayesian model.	required
`n_candidates`	`int`	The number of candidates to propose (default is 1).	`1`

Returns:

Type	Description
`Tensor`	A tensor containing the proposed candidates.

Notes

This method proposes candidates for Bayesian Optimization by numerically optimizing the acquisition function using the trained model. It updates the state of the Turbo controller if used and calculates the optimization bounds.

Source code in xopt/generators/bayesian/bayesian_generator.py

def propose_candidates(self, model: Module, n_candidates: int = 1) -> Tensor:
    """
    Propose candidates using Bayesian Optimization.

    Parameters
    ----------
    model : Module
        The trained Bayesian model.
    n_candidates : int, optional
        The number of candidates to propose (default is 1).

    Returns
    -------
    Tensor
        A tensor containing the proposed candidates.

    Notes
    -----
    This method proposes candidates for Bayesian Optimization by numerically
    optimizing the acquisition function using the trained model. It updates the
    state of the Turbo controller if used and calculates the optimization bounds.
    """
    # update TurBO state if used with the last `n_candidates` points
    if self.turbo_controller is not None:
        self.turbo_controller.update_state(self, n_candidates)

    # calculate optimization bounds
    bounds = self._get_optimization_bounds()

    # get acquisition function
    acq_funct = self.get_acquisition(model)

    # get initial candidates to start acquisition function optimization
    initial_points = self._get_initial_conditions(n_candidates)

    # get candidates -- grid optimizer does not support batch_initial_conditions
    if isinstance(self.numerical_optimizer, GridOptimizer):
        candidates = self.numerical_optimizer.optimize(
            acq_funct, bounds, n_candidates
        )
    else:
        candidates = self.numerical_optimizer.optimize(
            acq_funct, bounds, n_candidates, batch_initial_conditions=initial_points
        )
    return candidates

`train_model(data=None, update_internal=True)` ¶

Train a Bayesian model for Bayesian Optimization.

Parameters:

Name	Type	Description	Default
`data`	`DataFrame`	The data to be used for training the model. If not provided, the internal data of the generator is used.	`None`
`update_internal`	`bool`	Flag to indicate whether to update the internal model of the generator with the trained model (default is True).	`True`

Returns:

Type	Description
`Module`	The trained Bayesian model.

Raises:

Type	Description
`ValueError`	If no data is available to build the model.

Notes

This method trains a Bayesian model using the provided data or the internal data of the generator. It updates the internal model with the trained model if the 'update_internal' flag is set to True.

Source code in xopt/generators/bayesian/bayesian_generator.py

def train_model(
    self, data: pd.DataFrame | None = None, update_internal: bool = True
) -> Module:
    """
    Train a Bayesian model for Bayesian Optimization.

    Parameters
    ----------
    data : pd.DataFrame, optional
        The data to be used for training the model. If not provided, the internal
        data of the generator is used.
    update_internal : bool, optional
        Flag to indicate whether to update the internal model of the generator
        with the trained model (default is True).

    Returns
    -------
    Module
        The trained Bayesian model.

    Raises
    ------
    ValueError
        If no data is available to build the model.

    Notes
    -----
    This method trains a Bayesian model using the provided data or the internal
    data of the generator. It updates the internal model with the trained model
    if the 'update_internal' flag is set to True.
    """
    if data is None:
        data = self.get_training_data(self.data)
        if data is None:
            raise ValueError("no data available to build model")

    if data.empty:
        raise ValueError("no data available to build model")

    # get input bounds
    variable_bounds = {
        name: ele.domain for name, ele in self.vocs.variables.items()
    }

    # if turbo restrict points is true then set the bounds to the trust region
    # bounds
    if self.turbo_controller is not None:
        if self.turbo_controller.restrict_model_data:
            variable_bounds = dict(
                zip(
                    self.vocs.variable_names,
                    self.turbo_controller.get_trust_region(self).numpy().T,
                )
            )

    # add fixed feature bounds if requested
    if self.fixed_features is not None:
        # get bounds for each fixed_feature (vocs bounds take precedent)
        for key in self.fixed_features:
            if key not in variable_bounds:
                if key not in data:
                    raise KeyError(
                        "generator data needs to contain fixed feature "
                        f"column name `{key}`"
                    )
                f_data = data[key]
                bounds = [f_data.min(), f_data.max()]
                if bounds[1] - bounds[0] < 1e-8:
                    bounds[1] = bounds[0] + 1e-8
                variable_bounds[key] = bounds

    _model = self.gp_constructor.build_model(
        self.model_input_names,
        self.vocs.output_names,
        data,
        {name: variable_bounds[name] for name in self.model_input_names},
        **self.tkwargs,
    )

    if update_internal:
        self.model = _model

    return _model

`validate_turbo_controller(value, info)` `classmethod` ¶

note default behavior is no use of turbo

Source code in xopt/generators/bayesian/bayesian_generator.py

@field_validator("turbo_controller", mode="before")
@classmethod
def validate_turbo_controller(cls, value: Any, info: ValidationInfo):
    """note default behavior is no use of turbo"""
    if value is None:
        return value

    compatible_turbo_controllers = [
        turbo_controller
        for turbo_controller in cls.get_compatible_turbo_controllers()
        if turbo_controller is not None
    ]

    if len(compatible_turbo_controllers) == 0:
        raise ValueError("no turbo controllers are compatible with this generator")
    else:
        return validate_turbo_controller_base(
            value, compatible_turbo_controllers, info
        )

`visualize_model(**kwargs)` ¶

Display GP model predictions for the selected output(s).

The GP models are displayed with respect to the named variables. If None are given, the list of variables in vocs is used. Feasible samples are indicated with a filled orange "o", infeasible samples with a hollow red "o". Feasibility is calculated with respect to all constraints unless the selected output is a constraint itself, in which case only that one is considered.

Parameters:

Name	Type	Description	Default
`**kwargs`		Supported keyword arguments: - output_names : List[str] Outputs for which the GP models are displayed. Defaults to all outputs in vocs. - variable_names : List[str] The variables with respect to which the GP models are displayed (maximum of 2). Defaults to vocs.variable_names. - idx : int Index of the last sample to use. This also selects the point of reference in higher dimensions unless an explicit reference_point is given. - reference_point : dict Reference point determining the value of variables in vocs.variable_names, but not in variable_names (slice plots in higher dimensions). Defaults to last used sample. - show_samples : bool, optional Whether samples are shown. - show_prior_mean : bool, optional Whether the prior mean is shown. - show_feasibility : bool, optional Whether the feasibility region is shown. - show_acquisition : bool, optional Whether the acquisition function is computed and shown (only if acquisition function is not None). - n_grid : int, optional Number of grid points per dimension used to display the model predictions. - axes : Axes, optional Axes object used for plotting. - exponentiate : bool, optional Flag to exponentiate acquisition function before plotting.	`{}`

Returns:

Name	Type	Description
`result`	`tuple`	The matplotlib figure and axes objects.

Source code in xopt/generators/bayesian/bayesian_generator.py

def visualize_model(self, **kwargs):
    """Display GP model predictions for the selected output(s).

    The GP models are displayed with respect to the named variables. If None are given, the list of variables in
    vocs is used. Feasible samples are indicated with a filled orange "o", infeasible samples with a hollow
    red "o". Feasibility is calculated with respect to all constraints unless the selected output is a
    constraint itself, in which case only that one is considered.

    Parameters
    ----------
    **kwargs: dict, optional
        Supported keyword arguments:
        - output_names : List[str]
            Outputs for which the GP models are displayed. Defaults to all outputs in vocs.
        - variable_names : List[str]
            The variables with respect to which the GP models are displayed (maximum of 2).
            Defaults to vocs.variable_names.
        - idx : int
            Index of the last sample to use. This also selects the point of reference in
            higher dimensions unless an explicit reference_point is given.
        - reference_point : dict
            Reference point determining the value of variables in vocs.variable_names, but not in variable_names
            (slice plots in higher dimensions). Defaults to last used sample.
        - show_samples : bool, optional
            Whether samples are shown.
        - show_prior_mean : bool, optional
            Whether the prior mean is shown.
        - show_feasibility : bool, optional
            Whether the feasibility region is shown.
        - show_acquisition : bool, optional
            Whether the acquisition function is computed and shown (only if acquisition function is not None).
        - n_grid : int, optional
            Number of grid points per dimension used to display the model predictions.
        - axes : Axes, optional
            Axes object used for plotting.
        - exponentiate : bool, optional
            Flag to exponentiate acquisition function before plotting.

    Returns
    -------
    result : tuple
        The matplotlib figure and axes objects.
    """
    return visualize_generator_model(self, **kwargs)

`yaml(**kwargs)` ¶

serialize first then dump to yaml string

Source code in xopt/pydantic.py

def yaml(self, **kwargs):
    """serialize first then dump to yaml string"""
    output = json.loads(
        self.to_json(
            **kwargs,
        )
    )
    return yaml.dump(output)

`qPosteriorVariance` ¶

Bases: MCAcquisitionFunction

q-Posterior Variance acquisition function for Bayesian Optimization.

Parameters:

Name	Type	Description	Default
`model`	`Model`	A fitted model.	required
`sampler`	`Optional[MCSampler]`	The sampler used to draw base samples. Defaults to `SobolQMCNormalSampler(num_samples=512, collapse_batch_dims=True)`.	`None`
`objective`	`Optional[MCAcquisitionObjective]`	The MCAcquisitionObjective under which the samples are evaluated. Defaults to `IdentityMCObjective()`.	`None`
`posterior_transform`	`Optional[PosteriorTransform]`	A PosteriorTransform (optional).	`None`
`X_pending`	`Optional[Tensor]`	A `batch_shape x 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.	`None`

Methods:

Name	Description
`forward`	Evaluate qPosteriorVariance on the candidate set `X`.

Source code in xopt/generators/bayesian/bayesian_exploration.py

class qPosteriorVariance(MCAcquisitionFunction):
    """
    q-Posterior Variance acquisition function for Bayesian Optimization.

    Parameters
    ----------
    model : Model
        A fitted model.
    sampler : Optional[MCSampler]
        The sampler used to draw base samples. Defaults to `SobolQMCNormalSampler(num_samples=512, collapse_batch_dims=True)`.
    objective : Optional[MCAcquisitionObjective]
        The MCAcquisitionObjective under which the samples are evaluated. Defaults to `IdentityMCObjective()`.
    posterior_transform : Optional[PosteriorTransform]
        A PosteriorTransform (optional).
    X_pending : Optional[Tensor]
        A `batch_shape x 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.

    Methods
    -------
    forward(self, X: Tensor) -> Tensor
        Evaluate qPosteriorVariance on the candidate set `X`.
    """

    def __init__(
        self,
        model: Model,
        sampler: Optional[MCSampler] = None,
        objective: Optional[MCAcquisitionObjective] = None,
        posterior_transform: Optional[PosteriorTransform] = None,
        X_pending: Optional[Tensor] = None,
    ) -> None:
        super().__init__(
            model=model,
            sampler=sampler,
            objective=objective,
            posterior_transform=posterior_transform,
            X_pending=X_pending,
        )

    @concatenate_pending_points
    @t_batch_mode_transform()
    def forward(self, X: Tensor) -> Tensor:
        """
        Evaluate qPosteriorVariance on the candidate set `X`.

        Parameters
        ----------
        X : Tensor
            A `batch_shape x q x d`-dim Tensor of t-batches with `q` `d`-dim design points each.

        Returns
        -------
        Tensor
            A `batch_shape'`-dim Tensor of Posterior Variance values at the given design points `X`, where `batch_shape'` is the broadcasted batch shape of model and input `X`.
        """
        posterior = self.model.posterior(
            X=X, posterior_transform=self.posterior_transform
        )
        samples = self.sampler(posterior)
        obj = self.objective(samples, X=X)
        mean = obj.mean(dim=0)
        variance_samples = (obj - mean).abs()
        return variance_samples.max(dim=-1)[0].mean(dim=0)

`forward(X)` ¶

Evaluate qPosteriorVariance on the candidate set X.

Parameters:

Name	Type	Description	Default
`X`	`Tensor`	A `batch_shape x q x d`-dim Tensor of t-batches with `q` `d`-dim design points each.	required

Returns:

Type	Description
`Tensor`	A `batch_shape'`-dim Tensor of Posterior Variance values at the given design points `X`, where `batch_shape'` is the broadcasted batch shape of model and input `X`.

Source code in xopt/generators/bayesian/bayesian_exploration.py

@concatenate_pending_points
@t_batch_mode_transform()
def forward(self, X: Tensor) -> Tensor:
    """
    Evaluate qPosteriorVariance on the candidate set `X`.

    Parameters
    ----------
    X : Tensor
        A `batch_shape x q x d`-dim Tensor of t-batches with `q` `d`-dim design points each.

    Returns
    -------
    Tensor
        A `batch_shape'`-dim Tensor of Posterior Variance values at the given design points `X`, where `batch_shape'` is the broadcasted batch shape of model and input `X`.
    """
    posterior = self.model.posterior(
        X=X, posterior_transform=self.posterior_transform
    )
    samples = self.sampler(posterior)
    obj = self.objective(samples, X=X)
    mean = obj.mean(dim=0)
    variance_samples = (obj - mean).abs()
    return variance_samples.max(dim=-1)[0].mean(dim=0)

Bayesian Exploration Generator¶