skopt module
ScikitOptimize, or skopt
, is a simple and efficient library to
minimize (very) expensive and noisy blackbox functions. It implements
several methods for sequential modelbased optimization. skopt
is reusable
in many contexts and accessible.
Install
pip install scikitoptimize
Getting started
Find the minimum of the noisy function f(x)
over the range 2 < x < 2
with skopt
:
import numpy as np from skopt import gp_minimize def f(x): return (np.sin(5 * x[0]) * (1  np.tanh(x[0] ** 2)) * np.random.randn() * 0.1) res = gp_minimize(f, [(2.0, 2.0)])
For more read our introduction to bayesian optimization and the other examples.
Development
The library is still experimental and under heavy development.
The development version can be installed through:
git clone https://github.com/scikitoptimize/scikitoptimize.git cd scikitoptimize pip install r requirements.txt python setup.py develop
Run the tests by executing pytest
in the top level directory.
""" ScikitOptimize, or `skopt`, is a simple and efficient library to minimize (very) expensive and noisy blackbox functions. It implements several methods for sequential modelbased optimization. `skopt` is reusable in many contexts and accessible. [![Build Status](https://travisci.org/scikitoptimize/scikitoptimize.svg?branch=master)](https://travisci.org/scikitoptimize/scikitoptimize) ## Install ``` pip install scikitoptimize ``` ## Getting started Find the minimum of the noisy function `f(x)` over the range `2 < x < 2` with `skopt`: ```python import numpy as np from skopt import gp_minimize def f(x): return (np.sin(5 * x[0]) * (1  np.tanh(x[0] ** 2)) * np.random.randn() * 0.1) res = gp_minimize(f, [(2.0, 2.0)]) ``` For more read our [introduction to bayesian optimization](https://scikitoptimize.github.io/notebooks/bayesianoptimization.html) and the other [examples](https://github.com/scikitoptimize/scikitoptimize/tree/master/examples). ## Development The library is still experimental and under heavy development. The development version can be installed through: git clone https://github.com/scikitoptimize/scikitoptimize.git cd scikitoptimize pip install r requirements.txt python setup.py develop Run the tests by executing `pytest` in the top level directory. """ from . import acquisition from . import benchmarks from . import callbacks from . import learning from . import optimizer from . import plots from . import space from .optimizer import dummy_minimize from .optimizer import forest_minimize from .optimizer import gbrt_minimize from .optimizer import gp_minimize from .optimizer import Optimizer from .utils import load from .utils import dump from .utils import expected_minimum __version__ = "0.3" __all__ = ( "acquisition", "benchmarks", "callbacks", "learning", "optimizer", "plots", "space", "gp_minimize", "dummy_minimize", "forest_minimize", "gbrt_minimize", "Optimizer", "dump", "load", "expected_minimum" )
Functions
def dummy_minimize(
func, dimensions, n_calls=100, x0=None, y0=None, random_state=None, verbose=False, callback=None)
Random search by uniform sampling within the given bounds.
Parameters

func
[callable]: Function to minimize. Should take a array of parameters and return the function values. 
dimensions
[list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as a
(upper_bound, lower_bound)
tuple (forReal
orInteger
dimensions),  a
(upper_bound, lower_bound, prior)
tuple (forReal
dimensions),  as a list of categories (for
Categorical
dimensions), or  an instance of a
Dimension
object (Real
,Integer
orCategorical
).
 a

n_calls
[int, default=100]: Number of calls tofunc
to find the minimum. 
x0
[list, list of lists orNone
]: 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 orNone
]: Evaluation of initial input points. If it is a list, then it corresponds to evaluations of the function
at each element of
x0
: the ith element ofy0
corresponds to the function evaluated at the ith element ofx0
.  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 ofx0
.
 If it is a list, then it corresponds to evaluations of the function
at each element of

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 thencallback(res)
is called after each call tofunc
. If list of callables, then each callable in the list is called.
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.x_iters
[list of lists]: location of function evaluation for each iteration.func_vals
[array]: function value for each iteration.space
[Space]: the optimisation 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
def dummy_minimize(func, dimensions, n_calls=100, x0=None, y0=None, random_state=None, verbose=False, callback=None): """Random search by uniform sampling within the given bounds. Parameters  * `func` [callable]: Function to minimize. Should take a array of parameters and return the function values. * `dimensions` [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as  a `(upper_bound, lower_bound)` tuple (for `Real` or `Integer` dimensions),  a `(upper_bound, lower_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`). * `n_calls` [int, default=100]: Number of calls to `func` to find the minimum. * `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 ith element of `y0` corresponds to the function evaluated at the ith 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. 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.  `x_iters` [list of lists]: location of function evaluation for each iteration.  `func_vals` [array]: function value for each iteration.  `space` [Space]: the optimisation 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 """ # Save call args specs = {"args": copy.copy(inspect.currentframe().f_locals), "function": inspect.currentframe().f_code.co_name} # Check params rng = check_random_state(random_state) space = Space(dimensions) if x0 is None: x0 = [] elif not isinstance(x0[0], list): x0 = [x0] if not isinstance(x0, list): raise ValueError("`x0` should be a list, got %s" % type(x0)) n_init_func_calls = 0 if len(x0) > 0 and y0 is not None: if isinstance(y0, Iterable): y0 = list(y0) elif isinstance(y0, numbers.Number): y0 = [y0] else: raise ValueError("`y0` should be an iterable or a scalar, got %s" % type(y0)) if len(x0) != len(y0): raise ValueError("`x0` and `y0` should have the same length") if not all(map(np.isscalar, y0)): raise ValueError("`y0` elements should be scalars") elif len(x0) > 0 and y0 is None: y0 = [] n_calls = len(x0) n_init_func_calls = len(x0) elif len(x0) == 0 and y0 is not None: raise ValueError("`x0`cannot be `None` when `y0` is provided") else: # len(x0) == 0 and y0 is None y0 = [] callbacks = check_callback(callback) if verbose: callbacks.append(VerboseCallback( n_init=n_init_func_calls, n_total=n_calls)) X = x0 y = y0 # Random search X = X + space.rvs(n_samples=n_calls, random_state=rng) first = True result = None for i in range(len(y0), len(X)): y_i = func(X[i]) if first: first = False if not np.isscalar(y_i): raise ValueError("`func` should return a scalar") y.append(y_i) result = create_result(X[:i + 1], y, space, rng, specs) if eval_callbacks(callbacks, result): break y = np.array(y) return create_result(X, y, space, rng, specs)
def dump(
res, filename, store_objective=True, **kwargs)
Store an skopt optimization result into a file.
Parameters

res
[OptimizeResult
, scipy object]: Optimization result object to be stored. 
filename
[string orpathlib.Path
]: The path of the file in which it is to be stored. The compression method corresponding to one of the supported filename extensions ('.z', '.gz', '.bz2', '.xz' or '.lzma') will be used automatically. 
store_objective
[boolean, default=True]: Whether the objective function should be stored. Setstore_objective
toFalse
if your objective function (.specs['args']['func']
) is unserializable (i.e. if an exception is raised when trying to serialize the optimization result).Notice that if
store_objective
is set toFalse
, a deep copy of the optimization result is created, potentially leading to performance problems ifres
is very large. If the objective function is not critical, one can delete it before callingskopt.dump()
and thus avoid deep copying ofres
. 
**kwargs
[other keyword arguments]: All other keyword arguments will be passed tojoblib.dump
.
def dump(res, filename, store_objective=True, **kwargs): """ Store an skopt optimization result into a file. Parameters  * `res` [`OptimizeResult`, scipy object]: Optimization result object to be stored. * `filename` [string or `pathlib.Path`]: The path of the file in which it is to be stored. The compression method corresponding to one of the supported filename extensions ('.z', '.gz', '.bz2', '.xz' or '.lzma') will be used automatically. * `store_objective` [boolean, default=True]: Whether the objective function should be stored. Set `store_objective` to `False` if your objective function (`.specs['args']['func']`) is unserializable (i.e. if an exception is raised when trying to serialize the optimization result). Notice that if `store_objective` is set to `False`, a deep copy of the optimization result is created, potentially leading to performance problems if `res` is very large. If the objective function is not critical, one can delete it before calling `skopt.dump()` and thus avoid deep copying of `res`. * `**kwargs` [other keyword arguments]: All other keyword arguments will be passed to `joblib.dump`. """ if store_objective: dump_(res, filename, **kwargs) elif 'func' in res.specs['args']: # If the user does not want to store the objective and it is indeed # present in the provided object, then create a deep copy of it and # remove the objective function before dumping it with joblib.dump. res_without_func = deepcopy(res) del res_without_func.specs['args']['func'] dump_(res_without_func, filename, **kwargs) else: # If the user does not want to store the objective and it is already # missing in the provided object, dump it without copying. dump_(res, filename, **kwargs)
def expected_minimum(
res, n_random_starts=20, random_state=None)
Compute the minimum over the predictions of the last surrogate model.
Note that the returned minimum may not necessarily be an accurate prediction of the minimum of the true objective function.
Parameters

res
[OptimizeResult
, scipy object]: The optimization result returned by askopt
minimizer. 
n_random_starts
[int, default=20]: The number of random starts for the minimization of the surrogate model. 
random_state
[int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results.
Returns

x
[list]: location of the minimum. 
fun
[float]: the surrogate function value at the minimum.
def expected_minimum(res, n_random_starts=20, random_state=None): """ Compute the minimum over the predictions of the last surrogate model. Note that the returned minimum may not necessarily be an accurate prediction of the minimum of the true objective function. Parameters  * `res` [`OptimizeResult`, scipy object]: The optimization result returned by a `skopt` minimizer. * `n_random_starts` [int, default=20]: The number of random starts for the minimization of the surrogate model. * `random_state` [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results. Returns  * `x` [list]: location of the minimum. * `fun` [float]: the surrogate function value at the minimum. """ def func(x): reg = res.models[1] return reg.predict(x.reshape(1, 1))[0] xs = [res.x] if n_random_starts > 0: xs.extend(res.space.rvs(n_random_starts, random_state=random_state)) best_x = None best_fun = np.inf for x0 in xs: r = sp_minimize(func, x0=x0, bounds=res.space.bounds) if r.fun < best_fun: best_x = r.x best_fun = r.fun return [v for v in best_x], best_fun
def forest_minimize(
func, dimensions, base_estimator='ET', n_calls=100, n_random_starts=10, acq_func='EI', x0=None, y0=None, random_state=None, verbose=False, callback=None, n_points=10000, xi=0.01, kappa=1.96, n_jobs=1)
Sequential optimisation using decision trees.
A tree based regression model is used to model the 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_random_starts
evaluations.
Finally, n_calls  len(x0)  n_random_starts
evaluations are
made guided by the surrogate model. If x0
and y0
are both
provided then n_random_starts
evaluations are first made then
n_calls  n_random_starts
subsequent evaluations are made
guided by the surrogate model.
Parameters

func
[callable]: Function to minimize. Should take a array of parameters and return the function values. 
dimensions
[list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as a
(upper_bound, lower_bound)
tuple (forReal
orInteger
dimensions),  a
(upper_bound, lower_bound, prior)
tuple (forReal
dimensions),  as a list of categories (for
Categorical
dimensions), or  an instance of a
Dimension
object (Real
,Integer
orCategorical
).
NOTE: The upper and lower bounds are inclusive for
Integer
dimensions.  a

base_estimator
[string orRegressor
, default="ET"
]: The regressor to use as surrogate model. Can be either"RF"
for random forest regressor"ET"
for extra trees regressor instance of regressor with support for
return_std
in its predict method
The predefined models are initilized with good defaults. If you want to adjust the model parameters pass your own instance of a regressor which returns the mean and standard deviation when making predictions.

n_calls
[int, default=100]: Number of calls tofunc
. 
n_random_starts
[int, default=10]: Number of evaluations offunc
with random points before approximating it withbase_estimator
. 
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.

x0
[list, list of lists orNone
]: 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 orNone
]: Evaluation of initial input points. If it is a list, then it corresponds to evaluations of the function
at each element of
x0
: the ith element ofy0
corresponds to the function evaluated at the ith element ofx0
.  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 ofx0
.
 If it is a list, then it corresponds to evaluations of the function
at each element of

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, thencallback(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 forfit
andpredict
. If 1, then the number of jobs is set to the number of cores.
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.
For more details related to the OptimizeResult object, refer http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html
def forest_minimize(func, dimensions, base_estimator="ET", n_calls=100, n_random_starts=10, acq_func="EI", x0=None, y0=None, random_state=None, verbose=False, callback=None, n_points=10000, xi=0.01, kappa=1.96, n_jobs=1): """Sequential optimisation using decision trees. A tree based regression model is used to model the 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_random_starts` evaluations. Finally, `n_calls  len(x0)  n_random_starts` evaluations are made guided by the surrogate model. If `x0` and `y0` are both provided then `n_random_starts` evaluations are first made then `n_calls  n_random_starts` subsequent evaluations are made guided by the surrogate model. Parameters  * `func` [callable]: Function to minimize. Should take a array of parameters and return the function values. * `dimensions` [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as  a `(upper_bound, lower_bound)` tuple (for `Real` or `Integer` dimensions),  a `(upper_bound, lower_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` [string or `Regressor`, default=`"ET"`]: The regressor to use as surrogate model. Can be either  `"RF"` for random forest regressor  `"ET"` for extra trees regressor  instance of regressor with support for `return_std` in its predict method The predefined models are initilized with good defaults. If you want to adjust the model parameters pass your own instance of a regressor which returns the mean and standard deviation when making predictions. * `n_calls` [int, default=100]: Number of calls to `func`. * `n_random_starts` [int, default=10]: Number of evaluations of `func` with random points before approximating it with `base_estimator`. * `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. * `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 ith element of `y0` corresponds to the function evaluated at the ith 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. 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. For more details related to the OptimizeResult object, refer http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html """ rng = check_random_state(random_state) # Default estimator if isinstance(base_estimator, str): if base_estimator not in ("RF", "ET"): raise ValueError( "Valid strings for the base_estimator parameter" " are: 'RF' or 'ET', not '%s'" % base_estimator) if base_estimator == "RF": base_estimator = RandomForestRegressor(n_estimators=100, min_samples_leaf=3, n_jobs=n_jobs, random_state=rng) elif base_estimator == "ET": base_estimator = ExtraTreesRegressor(n_estimators=100, min_samples_leaf=3, n_jobs=n_jobs, random_state=rng) return base_minimize(func, dimensions, base_estimator, n_calls=n_calls, n_points=n_points, n_random_starts=n_random_starts, x0=x0, y0=y0, random_state=random_state, acq_func=acq_func, xi=xi, kappa=kappa, verbose=verbose, callback=callback, acq_optimizer="sampling")
def gbrt_minimize(
func, dimensions, base_estimator=None, n_calls=100, n_random_starts=10, acq_func='EI', 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)
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_random_starts
evaluations.
Finally, n_calls  len(x0)  n_random_starts
evaluations are
made guided by the surrogate model. If x0
and y0
are both
provided then n_random_starts
evaluations are first made then
n_calls  n_random_starts
subsequent evaluations are made
guided by the surrogate model.
Parameters

func
[callable]: Function to minimize. Should take a array of parameters and return the function values. 
dimensions
[list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as a
(upper_bound, lower_bound)
tuple (forReal
orInteger
dimensions),  a
(upper_bound, lower_bound, "prior")
tuple (forReal
dimensions),  as a list of categories (for
Categorical
dimensions), or  an instance of a
Dimension
object (Real
,Integer
orCategorical
).
 a

base_estimator
[GradientBoostingQuantileRegressor
]: The regressor to use as surrogate model 
n_calls
[int, default=100]: Number of calls tofunc
. 
n_random_starts
[int, default=10]: Number of evaluations offunc
with random points before approximating it withbase_estimator
. 
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.

x0
[list, list of lists orNone
]: 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 orNone
]: Evaluation of initial input points. If it is a list, then it corresponds to evaluations of the function
at each element of
x0
: the ith element ofy0
corresponds to the function evaluated at the ith element ofx0
.  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 ofx0
.
 If it is a list, then it corresponds to evaluations of the function
at each element of

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, thencallback(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 forfit
andpredict
. If 1, then the number of jobs is set to the number of cores.
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
def gbrt_minimize(func, dimensions, base_estimator=None, n_calls=100, n_random_starts=10, acq_func="EI", 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): """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_random_starts` evaluations. Finally, `n_calls  len(x0)  n_random_starts` evaluations are made guided by the surrogate model. If `x0` and `y0` are both provided then `n_random_starts` evaluations are first made then `n_calls  n_random_starts` subsequent evaluations are made guided by the surrogate model. Parameters  * `func` [callable]: Function to minimize. Should take a array of parameters and return the function values. * `dimensions` [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as  a `(upper_bound, lower_bound)` tuple (for `Real` or `Integer` dimensions),  a `(upper_bound, lower_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=10]: Number of evaluations of `func` with random points before approximating it with `base_estimator`. * `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. * `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 ith element of `y0` corresponds to the function evaluated at the ith 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. 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 """ # Check params rng = check_random_state(random_state) # Default estimator if base_estimator is None: gbrt = GradientBoostingRegressor(n_estimators=30, loss="quantile") base_estimator = GradientBoostingQuantileRegressor(base_estimator=gbrt, n_jobs=n_jobs, random_state=rng) return base_minimize(func, dimensions, base_estimator, n_calls=n_calls, n_points=n_points, n_random_starts=n_random_starts, x0=x0, y0=y0, random_state=random_state, xi=xi, kappa=kappa, acq_func=acq_func, verbose=verbose, callback=callback, acq_optimizer="sampling")
def gp_minimize(
func, dimensions, base_estimator=None, n_calls=100, n_random_starts=10, acq_func='gp_hedge', acq_optimizer='lbfgs', 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)
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 crossvalidation 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_random_starts
evaluations.
Finally, n_calls  len(x0)  n_random_starts
evaluations are
made guided by the surrogate model. If x0
and y0
are both
provided then n_random_starts
evaluations are first made then
n_calls  n_random_starts
subsequent evaluations are made
guided by the surrogate model.
Parameters

func
[callable]: Function to minimize. Should take a array of parameters and return the function values. 
dimensions
[list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as a
(upper_bound, lower_bound)
tuple (forReal
orInteger
dimensions),  a
(upper_bound, lower_bound, "prior")
tuple (forReal
dimensions),  as a list of categories (for
Categorical
dimensions), or  an instance of a
Dimension
object (Real
,Integer
orCategorical
).
NOTE: The upper and lower bounds are inclusive for
Integer
dimensions.  a

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 tofunc
. 
n_random_starts
[int, default=10]: Number of evaluations offunc
with random points before approximating it withbase_estimator
. 
acq_func
[string, default="EI"
]: 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
throughacq_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 bysoftmax(\eta g_i)
 After fitting the surrogate model with
(X_best, y_best)
, the gains are updated such thatg_i = \mu(X_i)
 Each acquisition function is optimised independently to propose an
candidate point
 The gains
Reference: https://dslpitt.org/uai/papers/11/p327hoffman.pdf

acq_optimizer
[string,"sampling"
or"lbfgs"
, default="lbfgs"
]: Method to minimize the acquistion function. The fit model is updated with the optimal value obtained by optimizingacq_func
withacq_optimizer
.The
acq_func
is computed atn_points
sampled randomly. If set to
"sampling"
, then the point among thesen_points
where theacq_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.
 The
 If set to

x0
[list, list of lists orNone
]: 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 orNone
] Evaluation of initial input points. If it is a list, then it corresponds to evaluations of the function
at each element of
x0
: the ith element ofy0
corresponds to the function evaluated at the ith element ofx0
.  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 ofx0
.
 If it is a list, then it corresponds to evaluations of the function
at each element of

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 thencallback(res)
is called after each call tofunc
. 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 whenacq_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 beforehand, this can be set directly to the variance of the noise.
 Set this to a value close to zero (1e10) if the function is noisefree. 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 whenacq_optimizer
is set to "lbfgs." Defaults to 1 core. Ifn_jobs=1
, then number of jobs is set to number of cores.
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
def gp_minimize(func, dimensions, base_estimator=None, n_calls=100, n_random_starts=10, acq_func="gp_hedge", acq_optimizer="lbfgs", 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): """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 crossvalidation 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_random_starts` evaluations. Finally, `n_calls  len(x0)  n_random_starts` evaluations are made guided by the surrogate model. If `x0` and `y0` are both provided then `n_random_starts` evaluations are first made then `n_calls  n_random_starts` subsequent evaluations are made guided by the surrogate model. Parameters  * `func` [callable]: Function to minimize. Should take a array of parameters and return the function values. * `dimensions` [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as  a `(upper_bound, lower_bound)` tuple (for `Real` or `Integer` dimensions),  a `(upper_bound, lower_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=10]: Number of evaluations of `func` with random points before approximating it with `base_estimator`. * `acq_func` [string, default=`"EI"`]: 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)` Reference: https://dslpitt.org/uai/papers/11/p327hoffman.pdf * `acq_optimizer` [string, `"sampling"` or `"lbfgs"`, default=`"lbfgs"`]: Method to minimize the acquistion 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 `"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 ith element of `y0` corresponds to the function evaluated at the ith 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 beforehand, this can be set directly to the variance of the noise.  Set this to a value close to zero (1e10) if the function is noisefree. 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. 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 """ # Check params rng = check_random_state(random_state) dim_types = [check_dimension(d) for d in dimensions] is_cat = all([isinstance(check_dimension(d), Categorical) for d in dim_types]) if is_cat: transformed_dims = [check_dimension(d, transform="identity") for d in dimensions] else: transformed_dims = [] for dim_type, dim in zip(dim_types, dimensions): if isinstance(dim_type, Categorical): transformed_dims.append( check_dimension(dim, transform="onehot") ) # To make sure that GP operates in the [0, 1] space else: transformed_dims.append( check_dimension(dim, transform="normalize") ) space = Space(transformed_dims) # Default GP if base_estimator is None: cov_amplitude = ConstantKernel(1.0, (0.01, 1000.0)) if is_cat: other_kernel = HammingKernel( length_scale=np.ones(space.transformed_n_dims)) acq_optimizer = "sampling" else: other_kernel = Matern( length_scale=np.ones(space.transformed_n_dims), length_scale_bounds=[(0.01, 100)] * space.transformed_n_dims, nu=2.5) base_estimator = GaussianProcessRegressor( kernel=cov_amplitude * other_kernel, normalize_y=True, random_state=rng, alpha=0.0, noise=noise, n_restarts_optimizer=2) return base_minimize( func, dimensions, base_estimator=base_estimator, acq_func=acq_func, xi=xi, kappa=kappa, acq_optimizer=acq_optimizer, n_calls=n_calls, n_points=n_points, n_random_starts=n_random_starts, n_restarts_optimizer=n_restarts_optimizer, x0=x0, y0=y0, random_state=random_state, verbose=verbose, callback=callback, n_jobs=n_jobs)
def load(
filename, **kwargs)
Reconstruct a skopt optimization result from a file persisted with skopt.dump.
Notice that the loaded optimization result can be missing
the objective function (.specs['args']['func']
) if dump
was called with store_objective=False
.
Parameters

filename
[string orpathlib.Path
]: The path of the file from which to load the optimization result. 
**kwargs
[other keyword arguments]: All other keyword arguments will be passed tojoblib.load
.
Returns
res
[OptimizeResult
, scipy object]: Reconstructed OptimizeResult instance.
def load(filename, **kwargs): """ Reconstruct a skopt optimization result from a file persisted with skopt.dump. Notice that the loaded optimization result can be missing the objective function (`.specs['args']['func']`) if `skopt.dump` was called with `store_objective=False`. Parameters  * `filename` [string or `pathlib.Path`]: The path of the file from which to load the optimization result. * `**kwargs` [other keyword arguments]: All other keyword arguments will be passed to `joblib.load`. Returns  * `res` [`OptimizeResult`, scipy object]: Reconstructed OptimizeResult instance. """ return load_(filename, **kwargs)
Classes
class Optimizer
Run bayesian optimisation loop.
An Optimizer
represents the steps of a bayesian optimisation loop. To
use it you need to provide your own loop mechanism. The various
optimisers provided by skopt
use this class under the hood.
Use this class directly if you want to control the iterations of your bayesian optimisation loop.
Parameters

dimensions
[list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as a
(upper_bound, lower_bound)
tuple (forReal
orInteger
dimensions),  a
(upper_bound, lower_bound, "prior")
tuple (forReal
dimensions),  as a list of categories (for
Categorical
dimensions), or  an instance of a
Dimension
object (Real
,Integer
orCategorical
).
 a

base_estimator
[sklearn regressor]: Should inherit fromsklearn.base.RegressorMixin
. In addition thepredict
method, should have an optionalreturn_std
argument, which returnsstd(Y  x)`` along with
E[Y  x]`. 
n_random_starts
[int, default=10]: DEPRECATED, usen_initial_points
instead. 
n_initial_points
[int, default=10]: Number of evaluations offunc
with initialization points before approximating it withbase_estimator
. Points provided asx0
count as initialization points. If len(x0) < n_initial_points additional points are sampled at random. 
acq_func
[string, default="EI"
]: Function to minimize over the posterior distribution. 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 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 $g_i = \mu(X_i)$
 Each acquisition function is optimised independently to
propose an candidate point
 The gains

acq_optimizer
[string,"sampling"
or"lbfgs"
, default="lbfgs"
]: Method to minimize the acquistion function. The fit model is updated with the optimal value obtained by optimizingacq_func
withacq_optimizer
. If set to
"sampling"
, thenacq_func
is optimized by computingacq_func
atn_points
randomly sampled points.  If set to
"lbfgs"
, thenacq_func
is optimized by Sampling
n_restarts_optimizer
points randomly. "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.
 Sampling
 If set to

random_state
[int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results. 
acq_func_kwargs
[dict]: Additional arguments to be passed to the acquistion function. 
acq_optimizer_kwargs
[dict]: Additional arguments to be passed to the acquistion optimizer.
Attributes
Xi
[list]: Points at which objective has been evaluated.yi
[scalar]: Values of objective at corresponding points inXi
.models
[list]: Regression models used to fit observations and compute acquisition function.space
An instance ofskopt.space.Space
. Stores parameter search space used to sample points, bounds, and type of parameters.
class Optimizer(object): """Run bayesian optimisation loop. An `Optimizer` represents the steps of a bayesian optimisation loop. To use it you need to provide your own loop mechanism. The various optimisers provided by `skopt` use this class under the hood. Use this class directly if you want to control the iterations of your bayesian optimisation loop. Parameters  * `dimensions` [list, shape=(n_dims,)]: List of search space dimensions. Each search dimension can be defined either as  a `(upper_bound, lower_bound)` tuple (for `Real` or `Integer` dimensions),  a `(upper_bound, lower_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` [sklearn regressor]: Should inherit from `sklearn.base.RegressorMixin`. In addition the `predict` method, should have an optional `return_std` argument, which returns `std(Y  x)`` along with `E[Y  x]`. * `n_random_starts` [int, default=10]: DEPRECATED, 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`. Points provided as `x0` count as initialization points. If len(x0) < n_initial_points additional points are sampled at random. * `acq_func` [string, default=`"EI"`]: Function to minimize over the posterior distribution. 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 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 $g_i = \mu(X_i)$ * `acq_optimizer` [string, `"sampling"` or `"lbfgs"`, default=`"lbfgs"`]: Method to minimize the acquistion function. The fit model is updated with the optimal value obtained by optimizing `acq_func` with `acq_optimizer`.  If set to `"sampling"`, then `acq_func` is optimized by computing `acq_func` at `n_points` randomly sampled points.  If set to `"lbfgs"`, then `acq_func` is optimized by  Sampling `n_restarts_optimizer` points randomly.  `"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. * `random_state` [int, RandomState instance, or None (default)]: Set random state to something other than None for reproducible results. * `acq_func_kwargs` [dict]: Additional arguments to be passed to the acquistion function. * `acq_optimizer_kwargs` [dict]: Additional arguments to be passed to the acquistion optimizer. Attributes  * `Xi` [list]: Points at which objective has been evaluated. * `yi` [scalar]: Values of objective at corresponding points in `Xi`. * `models` [list]: Regression models used to fit observations and compute acquisition function. * `space` An instance of `skopt.space.Space`. Stores parameter search space used to sample points, bounds, and type of parameters. """ def __init__(self, dimensions, base_estimator, n_random_starts=None, n_initial_points=10, acq_func="gp_hedge", acq_optimizer="lbfgs", random_state=None, acq_func_kwargs=None, acq_optimizer_kwargs=None): # Arguments that are just stored not checked self.acq_func = acq_func self.rng = check_random_state(random_state) self.acq_func_kwargs = acq_func_kwargs if self.acq_func == "gp_hedge": self.cand_acq_funcs_ = ["EI", "LCB", "PI"] self.gains_ = np.zeros(3) else: self.cand_acq_funcs_ = [self.acq_func] if acq_func_kwargs is None: acq_func_kwargs = dict() self.eta = acq_func_kwargs.get("eta", 1.0) if acq_optimizer_kwargs is None: acq_optimizer_kwargs = dict() self.n_points = acq_optimizer_kwargs.get("n_points", 10000) self.n_restarts_optimizer = acq_optimizer_kwargs.get( "n_restarts_optimizer", 5) n_jobs = acq_optimizer_kwargs.get("n_jobs", 1) self.acq_optimizer_kwargs = acq_optimizer_kwargs self.space = Space(dimensions) self.models = [] self.Xi = [] self.yi = [] self._cat_inds = [] self._non_cat_inds = [] for ind, dim in enumerate(self.space.dimensions): if isinstance(dim, Categorical): self._cat_inds.append(ind) else: self._non_cat_inds.append(ind) if n_random_starts is not None: warnings.warn(("n_random_starts will be removed in favour of " "n_initial_points."), DeprecationWarning) n_initial_points = n_random_starts self._check_arguments(base_estimator, n_initial_points, acq_optimizer) self.n_jobs = n_jobs # The cache of responses of `ask` method for n_points not None. # This ensures that multiple calls to `ask` with n_points set # return same sets of points. # The cache is reset to {} at every call to `tell`. self.cache_ = {} def _check_arguments(self, base_estimator, n_initial_points, acq_optimizer): """Check arguments for sanity.""" if not is_regressor(base_estimator): raise ValueError( "%s has to be a regressor." % base_estimator) self.base_estimator = base_estimator if n_initial_points < 0: raise ValueError( "Expected `n_initial_points` >= 0, got %d" % n_initial_points) self._n_initial_points = n_initial_points self.n_initial_points_ = n_initial_points if (isinstance(base_estimator, (ExtraTreesRegressor, RandomForestRegressor, GradientBoostingQuantileRegressor)) and not acq_optimizer == "sampling"): raise ValueError( "The treebased regressor {0} should run with " "acq_optimizer='sampling'".format(type(base_estimator))) if acq_optimizer not in ["lbfgs", "sampling"]: raise ValueError("Expected acq_optimizer to be 'lbfgs' or " "'sampling', got {0}".format(acq_optimizer)) self.acq_optimizer = acq_optimizer def copy(self, random_state=None): """Create a shallow copy of an instance of the optimizer. Parameters  * `random_state` [int, RandomState instance, or None (default)]: Set the random state of the copy. """ optimizer = Optimizer( dimensions=self.space.dimensions, base_estimator=self.base_estimator, n_initial_points=self.n_initial_points_, acq_func=self.acq_func, acq_optimizer=self.acq_optimizer, acq_func_kwargs=self.acq_func_kwargs, acq_optimizer_kwargs=self.acq_optimizer_kwargs, random_state=random_state, ) if hasattr(self, "gains_"): optimizer.gains_ = np.copy(self.gains_) if self.Xi: optimizer.tell(self.Xi, self.yi) return optimizer def ask(self, n_points=None, strategy="cl_min"): """Query point or multiple points at which objective should be evaluated. * `n_points` [int or None, default=None]: Number of points returned by the ask method. If the value is None, a single point to evaluate is returned. Otherwise a list of points to evaluate is returned of size n_points. This is useful if you can evaluate your objective in parallel, and thus obtain more objective function evaluations per unit of time. * `strategy` [string, default=`"cl_min"`]: Method to use to sample multiple points (see also `n_points` description). This parameter is ignored if n_points = None. Supported options are `"cl_min"`, `"cl_mean"` or `"cl_max"`.  If set to `"cl_min"`, then constant liar strtategy is used with lie objective value being minimum of observed objective values. `"cl_mean"` and `"cl_max"` means mean and max of values respectively. For details on this strategy see: https://hal.archivesouvertes.fr/hal00732512/document With this strategy a copy of optimizer is created, which is then asked for a point, and the point is told to the copy of optimizer with some fake objective (lie), the next point is asked from copy, it is also told to the copy with fake objective and so on. The type of lie defines different flavours of `cl_x` strategies. """ if n_points is None: return self._ask() supported_strategies = ["cl_min", "cl_mean", "cl_max"] if not (isinstance(n_points, int) and n_points > 0): raise ValueError( "n_points should be int > 0, got " + str(n_points) ) if strategy not in supported_strategies: raise ValueError( "Expected parallel_strategy to be one of " + str(supported_strategies) + ", " + "got %s" % strategy ) # Caching the result with n_points not None. If some new parameters # are provided to the ask, the cache_ is not used. if (n_points, strategy) in self.cache_: return self.cache_[(n_points, strategy)] # Copy of the optimizer is made in order to manage the # deletion of points with "lie" objective (the copy of # oiptimizer is simply discarded) opt = self.copy() X = [] for i in range(n_points): x = opt.ask() X.append(x) if strategy == "cl_min": y_lie = np.min(opt.yi) if opt.yi else 0.0 # CLmin lie elif strategy == "cl_mean": y_lie = np.mean(opt.yi) if opt.yi else 0.0 # CLmax lie else: y_lie = np.max(opt.yi) if opt.yi else 0.0 # CLmax lie opt.tell(x, y_lie) # lie to the optimizer self.cache_ = {(n_points, strategy): X} # cache_ the result return X def _ask(self): """Suggest next point at which to evaluate the objective. Return a random point while not at least `n_initial_points` observations have been `tell`ed, after that `base_estimator` is used to determine the next point. """ if self._n_initial_points > 0: # this will not make a copy of `self.rng` and hence keep advancing # our random state. return self.space.rvs(random_state=self.rng)[0] else: if not self.models: raise RuntimeError("Random evaluations exhausted and no " "model has been fit.") next_x = self._next_x min_delta_x = min([self.space.distance(next_x, xi) for xi in self.Xi]) if abs(min_delta_x) <= 1e8: warnings.warn("The objective has been evaluated " "at this point before.") # return point computed from last call to tell() return next_x def tell(self, x, y, fit=True): """Record an observation (or several) of the objective function. Provide values of the objective function at points suggested by `ask()` or other points. By default a new model will be fit to all observations. The new model is used to suggest the next point at which to evaluate the objective. This point can be retrieved by calling `ask()`. To add observations without fitting a new model set `fit` to False. To add multiple observations in a batch pass a listoflists for `x` and a list of scalars for `y`. Parameters  * `x` [list or listoflists]: Point at which objective was evaluated. * `y` [scalar or list]: Value of objective at `x`. * `fit` [bool, default=True] Fit a model to observed evaluations of the objective. A model will only be fitted after `n_initial_points` points have been told to the optimizer irrespective of the value of `fit`. """ # if y isn't a scalar it means we have been handed a batch of points if (isinstance(y, Iterable) and all(isinstance(point, Iterable) for point in x)): if not np.all([p in self.space for p in x]): raise ValueError("Not all points are within the bounds of" " the space.") self.Xi.extend(x) self.yi.extend(y) self._n_initial_points = len(y) elif isinstance(x, Iterable) and isinstance(y, Number): if x not in self.space: raise ValueError("Point (%s) is not within the bounds of" " the space (%s)." % (x, self.space.bounds)) self.Xi.append(x) self.yi.append(y) self._n_initial_points = 1 else: raise ValueError("Type of arguments `x` (%s) and `y` (%s) " "not compatible." % (type(x), type(y))) # optimizer learned somethnig new  discard cache self.cache_ = {} # after being "told" n_initial_points we switch from sampling # random points to using a surrogate model if fit and self._n_initial_points <= 0: transformed_bounds = np.array(self.space.transformed_bounds) est = clone(self.base_estimator) with warnings.catch_warnings(): warnings.simplefilter("ignore") est.fit(self.space.transform(self.Xi), self.yi) if hasattr(self, "next_xs_") and self.acq_func == "gp_hedge": self.gains_ = est.predict(np.vstack(self.next_xs_)) self.models.append(est) X = self.space.transform(self.space.rvs( n_samples=self.n_points, random_state=self.rng)) self.next_xs_ = [] for cand_acq_func in self.cand_acq_funcs_: values = _gaussian_acquisition( X=X, model=est, y_opt=np.min(self.yi), acq_func=cand_acq_func, acq_func_kwargs=self.acq_func_kwargs) # Find the minimum of the acquisition function by randomly # sampling points from the space if self.acq_optimizer == "sampling": next_x = X[np.argmin(values)] # Use BFGS to find the mimimum of the acquisition function, the # minimization starts from `n_restarts_optimizer` different # points and the best minimum is used elif self.acq_optimizer == "lbfgs": x0 = X[np.argsort(values)[:self.n_restarts_optimizer]] with warnings.catch_warnings(): warnings.simplefilter("ignore") results = Parallel(n_jobs=self.n_jobs)( delayed(fmin_l_bfgs_b)( gaussian_acquisition_1D, x, args=(est, np.min(self.yi), cand_acq_func, self.acq_func_kwargs), bounds=self.space.transformed_bounds, approx_grad=False, maxiter=20) for x in x0) cand_xs = np.array([r[0] for r in results]) cand_acqs = np.array([r[1] for r in results]) next_x = cand_xs[np.argmin(cand_acqs)] # lbfgs should handle this but just in case there are # precision errors. if not self.space.is_categorical: next_x = np.clip( next_x, transformed_bounds[:, 0], transformed_bounds[:, 1]) self.next_xs_.append(next_x) if self.acq_func == "gp_hedge": logits = np.array(self.gains_) logits = np.max(logits) exp_logits = np.exp(self.eta * logits) probs = exp_logits / np.sum(exp_logits) next_x = self.next_xs_[np.argmax(self.rng.multinomial(1, probs))] else: next_x = self.next_xs_[0] # note the need for [0] at the end self._next_x = self.space.inverse_transform( next_x.reshape((1, 1)))[0] # Pack results return create_result(self.Xi, self.yi, self.space, self.rng, models=self.models) def run(self, func, n_iter=1): """Execute ask() + tell() `n_iter` times""" for _ in range(n_iter): x = self.ask() self.tell(x, func(x)) return create_result(self.Xi, self.yi, self.space, self.rng, models=self.models)
Ancestors (in MRO)
 Optimizer
 builtins.object
Static methods
def __init__(
self, dimensions, base_estimator, n_random_starts=None, n_initial_points=10, acq_func='gp_hedge', acq_optimizer='lbfgs', random_state=None, acq_func_kwargs=None, acq_optimizer_kwargs=None)
Initialize self. See help(type(self)) for accurate signature.
def __init__(self, dimensions, base_estimator, n_random_starts=None, n_initial_points=10, acq_func="gp_hedge", acq_optimizer="lbfgs", random_state=None, acq_func_kwargs=None, acq_optimizer_kwargs=None): # Arguments that are just stored not checked self.acq_func = acq_func self.rng = check_random_state(random_state) self.acq_func_kwargs = acq_func_kwargs if self.acq_func == "gp_hedge": self.cand_acq_funcs_ = ["EI", "LCB", "PI"] self.gains_ = np.zeros(3) else: self.cand_acq_funcs_ = [self.acq_func] if acq_func_kwargs is None: acq_func_kwargs = dict() self.eta = acq_func_kwargs.get("eta", 1.0) if acq_optimizer_kwargs is None: acq_optimizer_kwargs = dict() self.n_points = acq_optimizer_kwargs.get("n_points", 10000) self.n_restarts_optimizer = acq_optimizer_kwargs.get( "n_restarts_optimizer", 5) n_jobs = acq_optimizer_kwargs.get("n_jobs", 1) self.acq_optimizer_kwargs = acq_optimizer_kwargs self.space = Space(dimensions) self.models = [] self.Xi = [] self.yi = [] self._cat_inds = [] self._non_cat_inds = [] for ind, dim in enumerate(self.space.dimensions): if isinstance(dim, Categorical): self._cat_inds.append(ind) else: self._non_cat_inds.append(ind) if n_random_starts is not None: warnings.warn(("n_random_starts will be removed in favour of " "n_initial_points."), DeprecationWarning) n_initial_points = n_random_starts self._check_arguments(base_estimator, n_initial_points, acq_optimizer) self.n_jobs = n_jobs # The cache of responses of `ask` method for n_points not None. # This ensures that multiple calls to `ask` with n_points set # return same sets of points. # The cache is reset to {} at every call to `tell`. self.cache_ = {}
def ask(
self, n_points=None, strategy='cl_min')
Query point or multiple points at which objective should be evaluated.

n_points
[int or None, default=None]: Number of points returned by the ask method. If the value is None, a single point to evaluate is returned. Otherwise a list of points to evaluate is returned of size n_points. This is useful if you can evaluate your objective in parallel, and thus obtain more objective function evaluations per unit of time. 
strategy
[string, default="cl_min"
]: Method to use to sample multiple points (see alson_points
description). This parameter is ignored if n_points = None. Supported options are"cl_min"
,"cl_mean"
or"cl_max"
. If set to
"cl_min"
, then constant liar strtategy is used with lie objective value being minimum of observed objective values."cl_mean"
and"cl_max"
means mean and max of values respectively. For details on this strategy see:
https://hal.archivesouvertes.fr/hal00732512/document
With this strategy a copy of optimizer is created, which is then asked for a point, and the point is told to the copy of optimizer with some fake objective (lie), the next point is asked from copy, it is also told to the copy with fake objective and so on. The type of lie defines different flavours of
cl_x
strategies.  If set to
def ask(self, n_points=None, strategy="cl_min"): """Query point or multiple points at which objective should be evaluated. * `n_points` [int or None, default=None]: Number of points returned by the ask method. If the value is None, a single point to evaluate is returned. Otherwise a list of points to evaluate is returned of size n_points. This is useful if you can evaluate your objective in parallel, and thus obtain more objective function evaluations per unit of time. * `strategy` [string, default=`"cl_min"`]: Method to use to sample multiple points (see also `n_points` description). This parameter is ignored if n_points = None. Supported options are `"cl_min"`, `"cl_mean"` or `"cl_max"`.  If set to `"cl_min"`, then constant liar strtategy is used with lie objective value being minimum of observed objective values. `"cl_mean"` and `"cl_max"` means mean and max of values respectively. For details on this strategy see: https://hal.archivesouvertes.fr/hal00732512/document With this strategy a copy of optimizer is created, which is then asked for a point, and the point is told to the copy of optimizer with some fake objective (lie), the next point is asked from copy, it is also told to the copy with fake objective and so on. The type of lie defines different flavours of `cl_x` strategies. """ if n_points is None: return self._ask() supported_strategies = ["cl_min", "cl_mean", "cl_max"] if not (isinstance(n_points, int) and n_points > 0): raise ValueError( "n_points should be int > 0, got " + str(n_points) ) if strategy not in supported_strategies: raise ValueError( "Expected parallel_strategy to be one of " + str(supported_strategies) + ", " + "got %s" % strategy ) # Caching the result with n_points not None. If some new parameters # are provided to the ask, the cache_ is not used. if (n_points, strategy) in self.cache_: return self.cache_[(n_points, strategy)] # Copy of the optimizer is made in order to manage the # deletion of points with "lie" objective (the copy of # oiptimizer is simply discarded) opt = self.copy() X = [] for i in range(n_points): x = opt.ask() X.append(x) if strategy == "cl_min": y_lie = np.min(opt.yi) if opt.yi else 0.0 # CLmin lie elif strategy == "cl_mean": y_lie = np.mean(opt.yi) if opt.yi else 0.0 # CLmax lie else: y_lie = np.max(opt.yi) if opt.yi else 0.0 # CLmax lie opt.tell(x, y_lie) # lie to the optimizer self.cache_ = {(n_points, strategy): X} # cache_ the result return X
def copy(
self, random_state=None)
Create a shallow copy of an instance of the optimizer.
Parameters
random_state
[int, RandomState instance, or None (default)]: Set the random state of the copy.
def copy(self, random_state=None): """Create a shallow copy of an instance of the optimizer. Parameters  * `random_state` [int, RandomState instance, or None (default)]: Set the random state of the copy. """ optimizer = Optimizer( dimensions=self.space.dimensions, base_estimator=self.base_estimator, n_initial_points=self.n_initial_points_, acq_func=self.acq_func, acq_optimizer=self.acq_optimizer, acq_func_kwargs=self.acq_func_kwargs, acq_optimizer_kwargs=self.acq_optimizer_kwargs, random_state=random_state, ) if hasattr(self, "gains_"): optimizer.gains_ = np.copy(self.gains_) if self.Xi: optimizer.tell(self.Xi, self.yi) return optimizer
def run(
self, func, n_iter=1)
Execute ask() + tell() n_iter
times
def run(self, func, n_iter=1): """Execute ask() + tell() `n_iter` times""" for _ in range(n_iter): x = self.ask() self.tell(x, func(x)) return create_result(self.Xi, self.yi, self.space, self.rng, models=self.models)
def tell(
self, x, y, fit=True)
Record an observation (or several) of the objective function.
Provide values of the objective function at points suggested by ask()
or other points. By default a new model will be fit to all
observations. The new model is used to suggest the next point at
which to evaluate the objective. This point can be retrieved by calling
ask()
.
To add observations without fitting a new model set fit
to False.
To add multiple observations in a batch pass a listoflists for x
and a list of scalars for y
.
Parameters

x
[list or listoflists]: Point at which objective was evaluated. 
y
[scalar or list]: Value of objective atx
. 
fit
[bool, default=True] Fit a model to observed evaluations of the objective. A model will only be fitted aftern_initial_points
points have been told to the optimizer irrespective of the value offit
.
def tell(self, x, y, fit=True): """Record an observation (or several) of the objective function. Provide values of the objective function at points suggested by `ask()` or other points. By default a new model will be fit to all observations. The new model is used to suggest the next point at which to evaluate the objective. This point can be retrieved by calling `ask()`. To add observations without fitting a new model set `fit` to False. To add multiple observations in a batch pass a listoflists for `x` and a list of scalars for `y`. Parameters  * `x` [list or listoflists]: Point at which objective was evaluated. * `y` [scalar or list]: Value of objective at `x`. * `fit` [bool, default=True] Fit a model to observed evaluations of the objective. A model will only be fitted after `n_initial_points` points have been told to the optimizer irrespective of the value of `fit`. """ # if y isn't a scalar it means we have been handed a batch of points if (isinstance(y, Iterable) and all(isinstance(point, Iterable) for point in x)): if not np.all([p in self.space for p in x]): raise ValueError("Not all points are within the bounds of" " the space.") self.Xi.extend(x) self.yi.extend(y) self._n_initial_points = len(y) elif isinstance(x, Iterable) and isinstance(y, Number): if x not in self.space: raise ValueError("Point (%s) is not within the bounds of" " the space (%s)." % (x, self.space.bounds)) self.Xi.append(x) self.yi.append(y) self._n_initial_points = 1 else: raise ValueError("Type of arguments `x` (%s) and `y` (%s) " "not compatible." % (type(x), type(y))) # optimizer learned somethnig new  discard cache self.cache_ = {} # after being "told" n_initial_points we switch from sampling # random points to using a surrogate model if fit and self._n_initial_points <= 0: transformed_bounds = np.array(self.space.transformed_bounds) est = clone(self.base_estimator) with warnings.catch_warnings(): warnings.simplefilter("ignore") est.fit(self.space.transform(self.Xi), self.yi) if hasattr(self, "next_xs_") and self.acq_func == "gp_hedge": self.gains_ = est.predict(np.vstack(self.next_xs_)) self.models.append(est) X = self.space.transform(self.space.rvs( n_samples=self.n_points, random_state=self.rng)) self.next_xs_ = [] for cand_acq_func in self.cand_acq_funcs_: values = _gaussian_acquisition( X=X, model=est, y_opt=np.min(self.yi), acq_func=cand_acq_func, acq_func_kwargs=self.acq_func_kwargs) # Find the minimum of the acquisition function by randomly # sampling points from the space if self.acq_optimizer == "sampling": next_x = X[np.argmin(values)] # Use BFGS to find the mimimum of the acquisition function, the # minimization starts from `n_restarts_optimizer` different # points and the best minimum is used elif self.acq_optimizer == "lbfgs": x0 = X[np.argsort(values)[:self.n_restarts_optimizer]] with warnings.catch_warnings(): warnings.simplefilter("ignore") results = Parallel(n_jobs=self.n_jobs)( delayed(fmin_l_bfgs_b)( gaussian_acquisition_1D, x, args=(est, np.min(self.yi), cand_acq_func, self.acq_func_kwargs), bounds=self.space.transformed_bounds, approx_grad=False, maxiter=20) for x in x0) cand_xs = np.array([r[0] for r in results]) cand_acqs = np.array([r[1] for r in results]) next_x = cand_xs[np.argmin(cand_acqs)] # lbfgs should handle this but just in case there are # precision errors. if not self.space.is_categorical: next_x = np.clip( next_x, transformed_bounds[:, 0], transformed_bounds[:, 1]) self.next_xs_.append(next_x) if self.acq_func == "gp_hedge": logits = np.array(self.gains_) logits = np.max(logits) exp_logits = np.exp(self.eta * logits) probs = exp_logits / np.sum(exp_logits) next_x = self.next_xs_[np.argmax(self.rng.multinomial(1, probs))] else: next_x = self.next_xs_[0] # note the need for [0] at the end self._next_x = self.space.inverse_transform( next_x.reshape((1, 1)))[0] # Pack results return create_result(self.Xi, self.yi, self.space, self.rng, models=self.models)
Instance variables
var Xi
var acq_func
var acq_func_kwargs
var acq_optimizer_kwargs
var cache_
var eta
var models
var n_jobs
var n_points
var n_restarts_optimizer
var rng
var space
var yi