# Optimizer using Cross Entropy¶

## CrossEntropyOptimizer¶

class l2l.optimizers.crossentropy.optimizer.CrossEntropyOptimizer(traj, optimizee_create_individual, optimizee_fitness_weights, parameters, optimizee_bounding_func=None)[source]

Class for a generic cross entropy optimizer. In the pseudo code the algorithm does:

For n iterations do:
• Sample individuals from distribution
• evaluate individuals and get fitness
• pick rho * pop_size number of elite individuals
• Out of the remaining non-elite individuals, select them using a simulated-annealing style selection based on the difference between their fitness and the 1-rho quantile (gamma) fitness, and the current temperature
• Fit the distribution family to the new elite individuals by minimizing cross entropy. The distribution fitting is smoothed to prevent premature convergence to local minima. A weight equal to the smoothing parameter is assigned to the previous parameters when smoothing.

return final distribution parameters. (The final distribution parameters contain information regarding the location of the maxima)

Parameters: traj (Trajectory) – Use this trajectory to store the parameters of the specific runs. The parameters should be initialized based on the values in parameters optimizee_create_individual – Function that creates a new individual. All parameters of the Individual-Dict returned should be of numpy.float64 type optimizee_fitness_weights – Fitness weights. The fitness returned by the Optimizee is multiplied by these values (one for each element of the fitness vector) parameters – Instance of namedtuple() CrossEntropyParameters containing the parameters needed by the Optimizer
post_process(traj, fitnesses_results)[source]
end(traj)[source]

## CrossEntropyParameters¶

class l2l.optimizers.crossentropy.optimizer.CrossEntropyParameters

Bases: tuple

Parameters: pop_size – Minimal number of individuals per simulation. rho – Fraction of solutions to be considered elite in each iteration. smoothing – This is a factor between 0 and 1 that determines the weight assigned to the previous distribution parameters while calculating the new distribution parameters. The smoothing is done as a linear combination of the optimal parameters for the current data, and the previous distribution as follows: new_params = smoothing * old_params + (1 - smoothing) * optimal_new_params temp_decay – This parameter is the factor (necessarily between 0 and 1) by which the temperature decays each generation. To see the use of temperature, look at the documentation of CrossEntropyOptimizer n_iteration – Number of iterations to perform distribution – Distribution object to use. Has to implement a fit and sample function. Should be one of Gaussian, NoisyGaussian, BayesianGaussianMixture, NoisyBayesianGaussianMixture stop_criterion – (Optional) Stop if this fitness is reached. seed – The random seed used to sample and fit the distribution. CrossEntropyOptimizer uses a random generator seeded with this seed.
distribution
n_iteration
pop_size
rho
seed
smoothing
stop_criterion
temp_decay

## Distributions¶

class l2l.optimizers.crossentropy.distribution.Distribution[source]

Bases: object

Generic base for a distribution. Needs to implement the functions fit and sample.

init_random_state(random_state)[source]

Used to initialize the random number generator which is used to fit/sample data. Note that if the random_state is already set, this raises an AssertionError. The reason this is not a part of the constructor is that the distribution random state must be initialized only by the optimizer and not in the main function (where it is constructed). It is essential to call this function before using the distribution

Parameters: random_state – An instance of class:numpy.random.RandomState
fit(data_list)[source]

This function fits the distributions parameters to the given samples in maximum likelihood fashion.

Parameters: data_list – A list or array of individuals to fit to. a dict describing the current parametrization
sample(n_individuals)[source]

Samples n_individuals from the current parametrized distribution.

Parameters: n_individuals – An integer specifying the amount of individuals to sample A list or array of n_individuals
get_params()[source]
Returns: the parametrization of the distribution as a dict
class l2l.optimizers.crossentropy.distribution.Gaussian[source]

Gaussian distribution.

init_random_state(random_state)[source]

Used to initialize the random number generator which is used to fit/sample data. Note that if the random_state is already set, this raises an AssertionError. The reason this is not a part of the constructor is that the distribution random state must be initialized only by the optimizer and not in the main function (where it is constructed). It is essential to call this function before using the distribution

Parameters: random_state – An instance of class:numpy.random.RandomState
get_params()[source]
Returns: the parametrization of the distribution as a dict
fit(data_list, smooth_update=0)[source]

Fit a gaussian distribution to the given data

Parameters: data_list – list or numpy array with individuals as rows smooth_update – determines to which extent the new samples account for the new distribution. default is 0 -> old parameters are fully discarded specifying current parametrization
sample(n_individuals)[source]

Sample n_individuals individuals under the current parametrization

Parameters: n_individuals – number of individuals to sample. numpy array with n_individual rows of individuals
class l2l.optimizers.crossentropy.distribution.NoisyGaussian(noise_magnitude=1.0, coordinate_scale=None, noise_decay=0.95)[source]

Additive Noisy Gaussian distribution. The initialization of its noise components happens during the first fit where the magnitude of the noise in each diagonalized component is estimated.

Parameters: noise_magnitude – scalar factor that affects the magnitude of noise applied on the distribution parameters coordinate_scale – This should be a vector representing the scaling of the coordinates. The noise applied to each coordinate i is noise_magnitude*coordinate_scale[i] noise_decay – Multiplicative decay of the noise components
get_params()[source]
Returns: the parametrization of the distribution as a dict
fit(data_list, smooth_update=0)[source]

Fits the parameters to the given data (see Gaussian) and additionally adds noise in form of variance to the covariance matrix. Also, the noise is decayed after each step

Parameters: data_list – Data to be fitted to smooth_update – Smooth the parameter update with regard to the previous configuration describing parameter configuration
sample(n_individuals)[source]

Samples from current parametrization

Returns: n_individuals Individuals
class l2l.optimizers.crossentropy.distribution.BayesianGaussianMixture(n_components=2, **kwargs)[source]

BayesianGaussianMixture from sklearn

Unlike normal Gaussian mixture, the algorithm has tendency to set the weights of non present modes close to zero. Meaning that it effectively inferences the number of active modes present in the given data.

Parameters: n_components – components of the mixture model kwargs – Additional arguments that get passed on to sklearn.mixture.BayesianGaussianMixture
init_random_state(random_state)[source]

Used to initialize the random number generator which is used to fit/sample data. Note that if the random_state is already set, this raises an AssertionError. The reason this is not a part of the constructor is that the distribution random state must be initialized only by the optimizer and not in the main function (where it is constructed). It is essential to call this function before using the distribution

Parameters: random_state – An instance of class:numpy.random.RandomState
get_params()[source]
Returns: the parametrization of the distribution as a dict
fit(data_list, smooth_update=0)[source]

Fits data_list on the parametrized model

Parameters: data_list – list or numpy array with individuals as rows smooth_update – determines to which extent the new samples account for the new distribution. dict specifiying current parametrization
sample(n_individuals)[source]

Sample n_individuals individuals under the current parametrization

Parameters: n_individuals – number of individuals to sample numpy array with n_individuals rows of individuals
class l2l.optimizers.crossentropy.distribution.NoisyBayesianGaussianMixture(n_components, noise_magnitude=1.0, coordinate_scale=None, noise_decay=0.95, **kwargs)[source]

NoisyBayesianGaussianMixture is basically the same as BayesianGaussianMixture but superimposed with noise

Parameters: n_components – number of components in the mixture model noise_magnitude – scalar factor that affects the magnitude of noise applied on the fitted distribution parameters+ coordinate_scale – This should be a vector representing the scaling of the coordinates. The noise applied to each coordinate i is noise_magnitude * coordinate_scale[i] Defaults to 1 for each coordinate. noise_decay – factor that will decay the additive noise kwargs – additional arguments that get passed on to BayesianGaussianMixture distribution
get_params()[source]
Returns: the parametrization of the distribution as a dict