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# Source code for skopt.optimizer.gbrt

    from sklearn.utils import check_random_state

    from ..utils import cook_estimator
    from .base import base_minimize

    def gbrt_minimize(
        func,
        dimensions,
        base_estimator=None,
        n_calls=100,
        n_random_starts=None,
        n_initial_points=10,
        initial_point_generator="random",
        acq_func="LCB",
        acq_optimizer="auto",
        x0=None,
        y0=None,
        random_state=None,
        verbose=False,
        callback=None,
        n_points=10000,
        xi=0.01,
        kappa=1.96,
        n_jobs=1,
        model_queue_size=None,
        space_constraint=None,
    ):
        """Sequential optimization using gradient boosted trees.

        Gradient boosted regression trees are used to model the (very)
        expensive to evaluate function `func`. The model is improved
        by sequentially evaluating the expensive function at the next
        best point. Thereby finding the minimum of `func` with as
        few evaluations as possible.

        The total number of evaluations, `n_calls`, are performed like the
        following. If `x0` is provided but not `y0`, then the elements of `x0`
        are first evaluated, followed by `n_initial_points` evaluations.
        Finally, `n_calls - len(x0) - n_initial_points` evaluations are
        made guided by the surrogate model. If `x0` and `y0` are both
        provided then `n_initial_points` evaluations are first made then
        `n_calls - n_initial_points` subsequent evaluations are made
        guided by the surrogate model.

        The first `n_initial_points` are generated by the
        `initial_point_generator`.

        Parameters
        ----------
        func : callable
            Function to minimize. Should take a single list of parameters
            and return the objective value.

            If you have a search-space where all dimensions have names,
            then you can use `skopt.utils.use_named_args` as a decorator
            on your objective function, in order to call it directly
            with the named arguments. See `use_named_args` for an example.

        dimensions : list, shape (n_dims,)
            List of search space dimensions.
            Each search dimension can be defined either as

            - a `(lower_bound, upper_bound)` tuple (for `Real` or `Integer`
              dimensions),
            - a `(lower_bound, upper_bound, "prior")` tuple (for `Real`
              dimensions),
            - as a list of categories (for `Categorical` dimensions), or
            - an instance of a `Dimension` object (`Real`, `Integer` or
              `Categorical`).

        base_estimator : `GradientBoostingQuantileRegressor`
            The regressor to use as surrogate model

        n_calls : int, default: 100
            Number of calls to `func`.

        n_random_starts : int, default: None
            Number of evaluations of `func` with random points before
            approximating it with `base_estimator`.

            .. deprecated:: 0.8
                use `n_initial_points` instead.

        n_initial_points : int, default: 10
            Number of evaluations of `func` with initialization points
            before approximating it with `base_estimator`. Initial point
            generator can be changed by setting `initial_point_generator`.

        initial_point_generator : str, InitialPointGenerator instance, \
                default: `"random"`
            Sets a initial points generator. Can be either

            - `"random"` for uniform random numbers,
            - `"sobol"` for a Sobol' sequence,
            - `"halton"` for a Halton sequence,
            - `"hammersly"` for a Hammersly sequence,
            - `"lhs"` for a latin hypercube sequence,
            - `"grid"` for a uniform grid sequence

        acq_func : string, default: `"LCB"`
            Function to minimize over the forest posterior. Can be either

            - `"LCB"` for lower confidence bound.
            - `"EI"` for negative expected improvement.
            - `"PI"` for negative probability of improvement.
            - ``"EIps"`` for negated expected improvement per second to take into
              account the function compute time. Then, the objective function is
              assumed to return two values, the first being the objective value and
              the second being the time taken.
            - `"PIps"` for negated probability of improvement per second.

        x0 : list, list of lists or `None`
            Initial input points.

            - If it is a list of lists, use it as a list of input points.
            - If it is a list, use it as a single initial input point.
            - If it is `None`, no initial input points are used.

        y0 : list, scalar or `None`
            Evaluation of initial input points.

            - If it is a list, then it corresponds to evaluations of the function
              at each element of `x0` : the i-th element of `y0` corresponds
              to the function evaluated at the i-th element of `x0`.
            - If it is a scalar, then it corresponds to the evaluation of the
              function at `x0`.
            - If it is None and `x0` is provided, then the function is evaluated
              at each element of `x0`.

        random_state : int, RandomState instance, or None (default)
            Set random state to something other than None for reproducible
            results.

        verbose : boolean, default: False
            Control the verbosity. It is advised to set the verbosity to True
            for long optimization runs.

        callback : callable, optional
            If provided, then `callback(res)` is called after call to func.

        n_points : int, default: 10000
            Number of points to sample when minimizing the acquisition function.

        xi : float, default: 0.01
            Controls how much improvement one wants over the previous best
            values. Used when the acquisition is either `"EI"` or `"PI"`.

        kappa : float, default: 1.96
            Controls how much of the variance in the predicted values should be
            taken into account. If set to be very high, then we are favouring
            exploration over exploitation and vice versa.
            Used when the acquisition is `"LCB"`.

        n_jobs : int, default: 1
            The number of jobs to run in parallel for `fit` and `predict`.
            If -1, then the number of jobs is set to the number of cores.

        model_queue_size : int or None, default: None
            Keeps list of models only as long as the argument given. In the
            case of None, the list has no capped length.

        space_constraint : callable or None, default: None
            Constraint function. Should take a single list of parameters
            (i.e. a point in space) and return True if the point satisfies
            the constraints.
            If None, the space is not conditionally constrained.

        Returns
        -------
        res : `OptimizeResult`, scipy object
            The optimization result returned as a OptimizeResult object.
            Important attributes are:

            - `x` [list]: location of the minimum.
            - `fun` [float]: function value at the minimum.
            - `models`: surrogate models used for each iteration.
            - `x_iters` [list of lists]: location of function evaluation for each
              iteration.
            - `func_vals` [array]: function value for each iteration.
            - `space` [Space]: the optimization space.
            - `specs` [dict]`: the call specifications.
            - `rng` [RandomState instance]: State of the random state
              at the end of minimization.

            For more details related to the OptimizeResult object, refer
            http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html

        .. seealso:: functions :class:`skopt.gp_minimize`,
            :class:`skopt.dummy_minimize`, :class:`skopt.forest_minimize`
        """
        # Check params
        rng = check_random_state(random_state)

        if base_estimator is None:
            base_estimator = cook_estimator("GBRT", random_state=rng, n_jobs=n_jobs)
        return base_minimize(
            func,
            dimensions,
            base_estimator,
            n_calls=n_calls,
            n_points=n_points,
            n_random_starts=n_random_starts,
            n_initial_points=n_initial_points,
            initial_point_generator=initial_point_generator,
            x0=x0,
            y0=y0,
            random_state=random_state,
            xi=xi,
            kappa=kappa,
            acq_func=acq_func,
            verbose=verbose,
            callback=callback,
            acq_optimizer="sampling",
            space_constraint=space_constraint,
            model_queue_size=model_queue_size,
            n_jobs=n_jobs,
        )