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# `skopt.optimizer`.gp_minimize

skopt.optimizer.gp_minimize(func, dimensions, base_estimator=None, n_calls=100, n_random_starts=None, n_initial_points=10, initial_point_generator='random', acq_func='gp_hedge', acq_optimizer='auto', x0=None, y0=None, random_state=None, verbose=False, callback=None, n_points=10000, n_restarts_optimizer=5, xi=0.01, kappa=1.96, noise='gaussian', n_jobs=1, model_queue_size=None, space_constraint=None)

  Bayesian optimization using Gaussian Processes.

  If every function evaluation is expensive, for instance when the parameters are the hyperparameters of a neural network and the function evaluation is the mean cross-validation score across ten folds, optimizing the hyperparameters by standard optimization routines would take for ever!

  The idea is to approximate the function using a Gaussian process. In other words the function values are assumed to follow a multivariate gaussian. The covariance of the function values are given by a GP kernel between the parameters. Then a smart choice to choose the next parameter to evaluate can be made by the acquisition function over the Gaussian prior which is much quicker to evaluate.

  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`).

      > Note

      > The upper and lower bounds are inclusive for `Integer` dimensions.

    base_estimator a Gaussian process estimator

      The Gaussian process estimator to use for optimization. By default, a Matern kernel is used with the following hyperparameters tuned.

      - All the length scales of the Matern kernel.

      - The covariance amplitude that each element is multiplied with.

      - Noise that is added to the matern kernel. The noise is assumed to be iid gaussian.

    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 since version 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,

    acq_func string, default: `"gp_hedge"`

      Function to minimize over the gaussian prior. Can be either

      - `"LCB"` for lower confidence bound.

      - `"EI"` for negative expected improvement.

      - `"PI"` for negative probability of improvement.

      - `"gp_hedge"` Probabilistically choose one of the above three acquisition functions at every iteration. The weightage given to these gains can be set by \(\eta\) through `acq_func_kwargs`.

        - The gains `g_i` are initialized to zero.

        - At every iteration,

          - Each acquisition function is optimised independently to propose an candidate point `X_i`.

          - Out of all these candidate points, the next point `X_best` is chosen by \(softmax(\eta g_i)\)

          - After fitting the surrogate model with `(X_best, y_best)`, the gains are updated such that \(g_i -= \mu(X_i)\)

      - `"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 in seconds.

      - `"PIps"` for negated probability of improvement per second. The return type of the objective function is assumed to be similar to that of `"EIps"`

    acq_optimizer string, `"sampling"` or `"lbfgs"`, default: `"lbfgs"`

      Method to minimize the acquisition function. The fit model is updated with the optimal value obtained by optimizing `acq_func` with `acq_optimizer`.

      The `acq_func` is computed at `n_points` sampled randomly.

      - If set to `"auto"`, then `acq_optimizer` is configured on the basis of the space searched over. If the space is Categorical then this is set to be `"sampling"`.

      - If set to `"sampling"`, then the point among these `n_points` where the `acq_func` is minimum is the next candidate minimum.

      - If set to `"lbfgs"`, then

        - The `n_restarts_optimizer` no. of points which the acquisition function is least are taken as start points.

        - `"lbfgs"` is run for 20 iterations with these points as initial points to find local minima.

        - The optimal of these local minima is used to update the prior.

    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, list of callables, optional

      If callable then `callback(res)` is called after each call to `func`. If list of callables, then each callable in the list is called.

    n_points int, default: 10000

      Number of points to sample to determine the next “best” point. Useless if acq_optimizer is set to `"lbfgs"`.

    n_restarts_optimizer int, default: 5

      The number of restarts of the optimizer when `acq_optimizer` is `"lbfgs"`.

    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"`.

    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"`.

    noise float, default: “gaussian”

      - Use noise=”gaussian” if the objective returns noisy observations. The noise of each observation is assumed to be iid with mean zero and a fixed variance.

      - If the variance is known before-hand, this can be set directly to the variance of the noise.

      - Set this to a value close to zero (1e-10) if the function is noise-free. Setting to zero might cause stability issues.

    n_jobs int, default: 1

      Number of cores to run in parallel while running the lbfgs optimizations over the acquisition function. Valid only when `acq_optimizer` is set to `"lbfgs"`. Defaults to 1 core. If `n_jobs=-1`, then number of jobs is set to 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

    See also

    functions `skopt.forest_minimize`, `skopt.dummy_minimize`, `skopt.gbrt_minimize`