Source code for l2l.optimizers.naturalevolutionstrategies.optimizer

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.naturalevolutionstrategies")

NaturalEvolutionStrategiesParameters = namedtuple('NaturalEvolutionStrategiesParameters', [
    'learning_rate_mu',
    'learning_rate_sigma',
    'mu',
    'sigma',
    'mirrored_sampling_enabled',
    'fitness_shaping_enabled',
    'pop_size',
    'n_iteration',
    'stop_criterion',
    'seed',
])

NaturalEvolutionStrategiesParameters.__doc__ = """
:param learning_rate_mu: Learning rate for mean of distribution
:param learning_rate_sigma: Learning rate for standard deviation of distribution
:param mu: Initial mean of search distribution
:param sigma: Initial standard deviation of search distribution
:param mirrored_sampling_enabled: Should we turn on mirrored sampling i.e. sampling both e and -e
:param fitness_shaping_enabled: Should we turn on fitness shaping i.e. using only top `fitness_shaping_ratio` to update
       current individual?
:param pop_size: Number of individuals per simulation.
:param n_iteration: Number of iterations to perform
:param stop_criterion: (Optional) Stop if this fitness is reached.
:param seed: The random seed used for generating new individuals
"""


[docs]class NaturalEvolutionStrategiesOptimizer(Optimizer): """ Class Implementing the separable natural evolution strategies optimizer in natural coordinates as in: Wierstra, D., Schaul, T., Peters, J., & Schmidhuber, J. (2008). Natural evolution strategies. In Evolutionary Computation, 2008. CEC 2008.(IEEE World Congress on Computational Intelligence) (pp. 3381-3387). Glasmachers, T., Schaul, T., Yi, S., Wierstra, D., & Schmidhuber, J. (2010). Exponential natural evolution strategies. In Proceedings of the 12th annual conference on Genetic and evolutionary computation (pp. 393-400). Wierstra, D., Schaul, T., Glasmachers, T., Sun, Y., Peters, J., & Schmidhuber, J. (2014). Natural evolution strategies. In Journal of Machine Learning Research, 15(1) (pp. 949-980). In the pseudo code the algorithm does: For n iterations do: - Sample individuals z from multinormal search distribution with parameters mu, sigma s <- sample from N(0,1) z <- mu + sigma * s - If mirrored sampling is enabled, also sample individuals with opposite perturbations s z <- [mu + sigma * s, mu - sigma * s] - evaluate individuals z and get fitnesses F_i(z) - Update the parameters of the search distribution as mu_{t+1} <- mu_{t+1} + eta_mu * sigma * sum(F_i * s_i) sigma_{t+1} <- sigma_t * exp(eta_sigma / 2 * sum(F_i * (s_i ** 2 - 1)) - If fitness shaping is enabled, F_i is replaced with the utility u_i in the previous step, which is calculated as: u_i = max(0, log(n/2 + 1) - log(k)) / sum_{k=1}^{n}{max(0, log(n/2 + 1) - log(k))} - 1 / n where k and i are the indices of the individuals in descending order of fitness F_i :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:`.NaturalEvolutionStrategiesParameters` 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 a parameter is set to `None`, use default value as described in Wierstra et al. (2014) if parameters.learning_rate_mu is None: learning_rate_mu = 1. else: learning_rate_mu = parameters.learning_rate_mu if parameters.learning_rate_sigma is None: learning_rate_sigma = (3 + np.log(len(parameters.mu))) / (5. * np.sqrt(len(parameters.mu))) else: learning_rate_sigma = parameters.learning_rate_sigma if parameters.pop_size is None: pop_size = 4 + int(np.floor(3 * np.log(len(parameters.mu)))) else: pop_size = parameters.pop_size if pop_size < 1: raise ValueError("pop_size needs to be greater than 0") # The following parameters are recorded traj.f_add_parameter('learning_rate_mu', learning_rate_mu, comment='Learning rate mu') traj.f_add_parameter('learning_rate_sigma', learning_rate_sigma, comment='Learning rate mu') traj.f_add_parameter('mu', parameters.mu, comment='Initial mean of search distribution') traj.f_add_parameter('sigma', parameters.sigma, comment='Initial standard deviation of search distribution') traj.f_add_parameter( 'mirrored_sampling_enabled', parameters.mirrored_sampling_enabled, comment='Flag to enable mirrored sampling') traj.f_add_parameter( 'fitness_shaping_enabled', parameters.fitness_shaping_enabled, comment='Flag to enable fitness shaping') traj.f_add_parameter( 'pop_size', pop_size, comment='Number of minimal individuals simulated in each run') 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( 'seed', np.uint32(parameters.seed), comment='Seed used for random number generation in optimizer') self.random_state = np.random.RandomState(traj.parameters.seed) self.current_individual_arr, self.optimizee_individual_dict_spec = dict_to_list( self.optimizee_create_individual(), get_dict_spec=True) traj.f_add_derived_parameter( 'dimension', self.current_individual_arr.shape, comment='The dimension of the parameter space of the optimizee') # 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 self.pop_size = pop_size # Population size is dynamic in FACE self.best_fitness_in_run = -np.inf self.best_individual_in_run = None # Set initial parameters of search distribution self.mu = traj.mu self.sigma = traj.sigma # Generate initial distribution self.current_perturbations = self._get_perturbations(traj) current_eval_pop_arr = (self.mu + self.sigma * self.current_perturbations).tolist() self.eval_pop = [list_to_dict(ind, self.optimizee_individual_dict_spec) for ind in current_eval_pop_arr] # Bounding function has to be applied AFTER the individual has been converted to a dict if optimizee_bounding_func is not None: self.eval_pop = [self.optimizee_bounding_func(ind) for ind in self.eval_pop] self.eval_pop_arr = np.array([dict_to_list(ind) for ind in self.eval_pop]) self._expand_trajectory(traj) def _get_perturbations(self, traj): perturbations = self.random_state.randn(traj.pop_size, *traj.dimension) if traj.mirrored_sampling_enabled: return np.vstack([perturbations, -perturbations]) return perturbations
[docs] def post_process(self, traj, fitnesses_results): """ See :meth:`~l2l.optimizers.optimizer.Optimizer.post_process` """ n_iteration, stop_criterion, fitness_shaping_enabled = \ traj.n_iteration, traj.stop_criterion, traj.fitness_shaping_enabled 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() # NOTE: It is necessary to clear the finesses_results to clear the data in the reference, and del # is used to make sure it's not used in the rest of this function fitnesses_results.clear() del fitnesses_results # Last fitness is for the previous `current_individual_arr` weighted_fitness_list = weighted_fitness_list[:-1] current_individual_fitness = weighted_fitness_list[-1] # 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_arr[fitness_sorting_indices] sorted_fitness = np.asarray(weighted_fitness_list)[fitness_sorting_indices] sorted_perturbations = self.current_perturbations[fitness_sorting_indices] self.best_individual_in_run = sorted_population[0] self.best_fitness_in_run = sorted_fitness[0] logger.info("-- End of generation %d --", self.g) logger.info(" Evaluated %d individuals", len(weighted_fitness_list) + 1) logger.info(' Best Fitness: %.4f', self.best_fitness_in_run) logger.info(' Average Fitness: %.4f', np.mean(sorted_fitness)) # ************************************************************************************************************** # 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 # best_fitness_in_run - The highest fitness among the individuals in the # evaluated generation # pop_size - Population size generation_result_dict = { 'generation': self.g, 'best_fitness_in_run': self.best_fitness_in_run, 'current_individual_fitness': current_individual_fitness, '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 `EvolutionStrategiesOptimizer::post_process()` " "for comments documenting these parameters" ) traj.results.generation_params.f_add_result( generation_name + '.distribution_params', {'mu': self.mu.copy(), 'sigma': self.sigma.copy()}, comment="These are the parameters of the distribution that underlies the" " currently evaluated generation") if fitness_shaping_enabled: fitnesses_to_fit = self._compute_utility(sorted_fitness) else: fitnesses_to_fit = sorted_fitness assert len(fitnesses_to_fit) == len(sorted_perturbations) # ************************************************************************************************************** # Update the parameters of the search distribution using the natural gradient in natural coordinates # ************************************************************************************************************** self.mu += traj.learning_rate_mu * traj.sigma * np.dot(fitnesses_to_fit, sorted_perturbations) self.sigma *= np.exp(traj.learning_rate_sigma / 2. * np.dot(fitnesses_to_fit, sorted_perturbations ** 2 - 1.)) # ************************************************************************************************************** # 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 self.eval_pop.clear() # check if to stop if self.g < n_iteration - 1 and self.best_fitness_in_run < stop_criterion: self.current_perturbations = self._get_perturbations(traj) current_eval_pop_arr = (self.mu + self.sigma * self.current_perturbations).tolist() self.eval_pop = [list_to_dict(ind, self.optimizee_individual_dict_spec) for ind in current_eval_pop_arr] # Bounding function has to be applied AFTER the individual has been converted to a dict if self.optimizee_bounding_func is not None: self.eval_pop = [self.optimizee_bounding_func(ind) for ind in self.eval_pop] self.eval_pop_arr = np.array([dict_to_list(ind) for ind in self.eval_pop]) self.g += 1 # Update generation counter self._expand_trajectory(traj)
def _compute_utility(self, sorted_fitness): n_individuals = len(sorted_fitness) sorted_utilities = np.array([max(0., np.log((n_individuals / 2) + 1) - np.log(i + 1)) for i in range(n_individuals)]) sorted_utilities /= np.sum(sorted_utilities) sorted_utilities -= (1. / n_individuals) return sorted_utilities
[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) ES optimization --")