import logging
from collections import namedtuple
import numpy as np
from l2l import dict_to_list, list_to_dict
from l2l.optimizers.optimizer import Optimizer
logger = logging.getLogger("optimizers.crossentropy")
CrossEntropyParameters = namedtuple('CrossEntropyParameters',
['pop_size', 'rho', 'smoothing', 'temp_decay', 'n_iteration', 'distribution',
'stop_criterion', 'seed'])
CrossEntropyParameters.__doc__ = """
:param pop_size: Minimal number of individuals per simulation.
:param rho: Fraction of solutions to be considered elite in each iteration.
:param 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
:param 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 :class:`.CrossEntropyOptimizer`
:param n_iteration: Number of iterations to perform
:param distribution: Distribution object to use. Has to implement a fit and sample function. Should be one of
:class:`~.Gaussian`, :class:`~.NoisyGaussian`, :class:`~.BayesianGaussianMixture`, :class:`~.NoisyBayesianGaussianMixture`
:param stop_criterion: (Optional) Stop if this fitness is reached.
:param seed: The random seed used to sample and fit the distribution. :class:`.CrossEntropyOptimizer`
uses a random generator seeded with this seed.
"""
[docs]class CrossEntropyOptimizer(Optimizer):
"""
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)
:param ~l2l.utils.trajectory.Trajectory traj:
Use this trajectory to store the parameters of the specific runs. The parameters should be
initialized based on the values in `parameters`
:param optimizee_create_individual:
Function that creates a new individual. All parameters of the Individual-Dict returned should be
of numpy.float64 type
:param optimizee_fitness_weights:
Fitness weights. The fitness returned by the Optimizee is multiplied by these values (one for each
element of the fitness vector)
:param parameters:
Instance of :func:`~collections.namedtuple` :class:`.CrossEntropyParameters` containing the
parameters needed by the Optimizer
"""
def __init__(self, traj, optimizee_create_individual, optimizee_fitness_weights, parameters,
optimizee_bounding_func=None):
super().__init__(traj, optimizee_create_individual=optimizee_create_individual,
optimizee_fitness_weights=optimizee_fitness_weights, parameters=parameters,
optimizee_bounding_func=optimizee_bounding_func)
self.optimizee_bounding_func = optimizee_bounding_func
if parameters.pop_size < 1:
raise Exception("pop_size needs to be greater than 0")
if parameters.smoothing >= 1 or parameters.smoothing < 0:
raise Exception("smoothing has to be in interval [0, 1)")
# The following parameters are recorded
traj.f_add_parameter('pop_size', parameters.pop_size,
comment='Number of minimal individuals simulated in each run')
traj.f_add_parameter('rho', parameters.rho,
comment='Fraction of individuals considered elite in each generation')
traj.f_add_parameter('n_iteration', parameters.n_iteration,
comment='Number of iterations to run')
traj.f_add_parameter('stop_criterion', parameters.stop_criterion,
comment='Stop if best individual reaches this fitness')
traj.f_add_parameter('smoothing', parameters.smoothing,
comment='Weight of old parameters in smoothing')
traj.f_add_parameter('temp_decay', parameters.temp_decay,
comment='Decay factor for temperature')
traj.f_add_parameter('seed', np.uint32(parameters.seed),
comment='Seed used for random number generation in optimizer')
self.random_state = np.random.RandomState(traj.parameters.seed)
temp_indiv, self.optimizee_individual_dict_spec = dict_to_list(self.optimizee_create_individual(),
get_dict_spec=True)
traj.f_add_derived_parameter('dimension', len(temp_indiv),
comment='The dimension of the parameter space of the optimizee')
traj.f_add_derived_parameter('n_elite', int(parameters.rho * parameters.pop_size),
comment='Number of samples to be considered as elite')
# Added a generation-wise parameter logging
traj.results.f_add_result_group('generation_params',
comment='This contains the optimizer parameters that are'
' common across a generation')
# The following parameters are recorded as generation parameters i.e. once per generation
self.g = 0 # the current generation
# This is the value above which the samples are considered elite in the
# current generation
self.gamma = -np.inf
self.T = 1 # This is the temperature used to filter evaluated samples in this run
self.pop_size = parameters.pop_size # Population size is dynamic in FACE
self.best_fitness_in_run = -np.inf
self.best_individual_in_run = None
# The first iteration does not pick the values out of the Gaussian distribution. It picks randomly
# (or at-least as randomly as optimizee_create_individual creates individuals)
# Note that this array stores individuals as an np.array of floats as opposed to Individual-Dicts
# This is because this array is used within the context of the cross entropy algorithm and
# Thus needs to handle the optimizee individuals as vectors
current_eval_pop = [self.optimizee_create_individual() for _ in range(parameters.pop_size)]
if optimizee_bounding_func is not None:
current_eval_pop = [self.optimizee_bounding_func(ind) for ind in current_eval_pop]
self.eval_pop = current_eval_pop
self.eval_pop_asarray = np.array([dict_to_list(x) for x in self.eval_pop])
# Max Likelihood
self.current_distribution = parameters.distribution
# Adding the distribution parameters
traj.f_add_parameter_group('distribution', comment="Parameters for the distribution class")
distribution_params = self.current_distribution.get_params()
for param_name, param_value in distribution_params.items():
traj.parameters.distribution.f_add_parameter(param_name, param_value)
self.current_distribution.init_random_state(self.random_state)
self.current_distribution.fit(self.eval_pop_asarray)
self._expand_trajectory(traj)
[docs] def post_process(self, traj, fitnesses_results):
"""
See :meth:`~l2l.optimizers.optimizer.Optimizer.post_process`
"""
n_iteration, smoothing, temp_decay = \
traj.n_iteration, traj.smoothing, traj.temp_decay
stop_criterion, n_elite = traj.stop_criterion, traj.n_elite
weighted_fitness_list = []
#**************************************************************************************************************
# Storing run-information in the trajectory
# Reading fitnesses and performing distribution update
#**************************************************************************************************************
for run_index, fitness in fitnesses_results:
# We need to convert the current run index into an ind_idx
# (index of individual within one generation)
traj.v_idx = run_index
ind_index = traj.par.ind_idx
traj.f_add_result('$set.$.individual', self.eval_pop[ind_index])
traj.f_add_result('$set.$.fitness', fitness)
weighted_fitness_list.append(np.dot(fitness, self.optimizee_fitness_weights))
traj.v_idx = -1 # set trajectory back to default
weighted_fitness_list = np.array(weighted_fitness_list).ravel()
# Performs descending arg-sort of weighted fitness
fitness_sorting_indices = list(reversed(np.argsort(weighted_fitness_list)))
# Sorting the data according to fitness
sorted_population = self.eval_pop_asarray[fitness_sorting_indices]
sorted_fitness = np.asarray(weighted_fitness_list)[fitness_sorting_indices]
# Elite individuals are with performance better than or equal to the (1-rho) quantile.
# See original describtion of cross entropy for optimization
elite_individuals = sorted_population[:n_elite]
self.best_individual_in_run = sorted_population[0]
self.best_fitness_in_run = sorted_fitness[0]
self.gamma = sorted_fitness[n_elite - 1]
logger.info("-- End of generation %d --", self.g)
logger.info(" Evaluated %d individuals", len(fitnesses_results))
logger.info(' Best Fitness: %.4f', self.best_fitness_in_run)
logger.info(' Average Fitness: %.4f', np.mean(sorted_fitness))
logger.debug(' Calculated gamma: %.4f', self.gamma)
#**************************************************************************************************************
# Storing Generation Parameters / Results in the trajectory
#**************************************************************************************************************
# These entries correspond to the generation that has been simulated prior to this post-processing run
# Documentation of algorithm parameters for the current generation
#
# generation - The index of the evaluated generation
# gamma - The fitness threshold inferred from the evaluated generation
# (This is used in sampling the next generation)
# T - Temperature used to select non-elite elements among the individuals
# of the evaluated generation
# best_fitness_in_run - The highest fitness among the individuals in the
# evaluated generation
# pop_size - Population size
generation_result_dict = {
'generation': self.g,
'gamma': self.gamma,
'T': self.T,
'best_fitness_in_run': self.best_fitness_in_run,
'average_fitness_in_run': np.mean(sorted_fitness),
'pop_size': self.pop_size
}
generation_name = 'generation_{}'.format(self.g)
traj.results.generation_params.f_add_result_group(generation_name)
traj.results.generation_params.f_add_result(
generation_name + '.algorithm_params', generation_result_dict,
comment="These are the parameters that correspond to the algorithm, look at the source code"
" for `CrossEntropyOptimizer::post_process()` for comments documenting these"
" parameters")
# new distribution fit
individuals_to_be_fitted = elite_individuals
# Temperature dependent sampling of non elite individuals
if temp_decay > 0:
# Keeping non-elite samples with certain probability dependent on temperature (like Simulated Annealing)
non_elite_selection_probs = np.clip(np.exp((weighted_fitness_list[n_elite:] - self.gamma) / self.T),
a_min=0.0, a_max=1.0)
non_elite_selected_indices = self.random_state.binomial(1, non_elite_selection_probs).astype(bool)
non_elite_eval_pop_asarray = sorted_population[n_elite:][non_elite_selected_indices]
individuals_to_be_fitted = np.concatenate((elite_individuals, non_elite_eval_pop_asarray))
# Fitting New distribution parameters.
self.distribution_results = self.current_distribution.fit(individuals_to_be_fitted, smoothing)
#Add the results of the distribution fitting to the trajectory
traj.results.generation_params.f_add_result(
generation_name + '.distribution_params', self.distribution_results,
comment="These are the parameters of the distribution inferred from the currently evaluated"
" generation")
#**************************************************************************************************************
# Create the next generation by sampling the inferred distribution
#**************************************************************************************************************
# Note that this is only done in case the evaluated run is not the last run
fitnesses_results.clear()
self.eval_pop.clear()
# check if to stop
if self.g < n_iteration - 1 and self.best_fitness_in_run < stop_criterion:
#Sample from the constructed distribution
self.eval_pop_asarray = self.current_distribution.sample(self.pop_size)
self.eval_pop = [list_to_dict(ind_asarray, self.optimizee_individual_dict_spec)
for ind_asarray in self.eval_pop_asarray]
# Clip to boundaries
if self.optimizee_bounding_func is not None:
self.eval_pop = [self.optimizee_bounding_func(individual) for individual in self.eval_pop]
self.eval_pop_asarray = np.array([dict_to_list(x) for x in self.eval_pop])
self.g += 1 # Update generation counter
self.T *= temp_decay
self._expand_trajectory(traj)
[docs] def end(self, traj):
"""
See :meth:`~l2l.optimizers.optimizer.Optimizer.end`
"""
best_last_indiv_dict = list_to_dict(self.best_individual_in_run.tolist(),
self.optimizee_individual_dict_spec)
traj.f_add_result('final_individual', best_last_indiv_dict)
traj.f_add_result('final_fitness', self.best_fitness_in_run)
traj.f_add_result('n_iteration', self.g + 1)
# ------------ Finished all runs and print result --------------- #
logger.info("-- End of (successful) CE optimization --")
logger.info("-- Final distribution parameters --")
for parameter_key, parameter_value in sorted(self.distribution_results.items()):
logger.info(' %s: %s', parameter_key, parameter_value)