Original Natural Evolution Strategy (ONES)

class pypop7.optimizers.nes.ones.ONES(problem, options)[source]

Original Natural Evolution Strategy (ONES).

Note

Here we include ONES mainly for benchmarking and/or theoretical purpose. In practice, more advanced versions (e.g., ENES, XNES, SNES, and R1NES) should be first considered rather than the original version, which was first published in IEEE CEC-2008 by Schmidhuber’s team. Simply speaking, the parameterized search distribution makes the mathematical derivation of the complex population update/evolution process possible and tractable, under mild assumptions.

Parameters:

  • problem (dict) –

    problem arguments with the following common settings (keys):

    • ’fitness_function’ - objective function to be minimized (func),

    • ’ndim_problem’ - number of dimensionality (int),

    • ’upper_boundary’ - upper boundary of search range (array_like),

    • ’lower_boundary’ - lower boundary of search range (array_like).

  • options (dict) –

    optimizer options with the following common settings (keys):

    • ’max_function_evaluations’ - maximum of function evaluations (int, default: np.inf),

    • ’max_runtime’ - maximal runtime to be allowed (float, default: np.inf),

    • ’seed_rng’ - seed for random number generation needed to be explicitly set (int);

    and with the following particular settings (keys):

    • ’n_individuals’ - number of offspring/descendants, aka offspring population size (int),

    • ’n_parents’ - number of parents/ancestors, aka parental population size (int),

    • ’mean’ - initial (starting) point (array_like),

      • If not given, it will draw a random sample from the uniform distribution whose search range is bounded by problem[‘lower_boundary’] and problem[‘upper_boundary’].

    • ’lr_mean’ - learning rate of distribution mean update (float, default: 1.0),

    • ’lr_sigma’ - learning rate of global step-size adaptation (float, default: 1.0).

Examples

Use the optimizer ONES to minimize the well-known test function Rosenbrock:

 1>>> import numpy  # engine for numerical computing
 2>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
 3>>> from pypop7.optimizers.nes.ones import ONES
 4>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
 5...            'ndim_problem': 2,
 6...            'lower_boundary': -5*numpy.ones((2,)),
 7...            'upper_boundary': 5*numpy.ones((2,))}
 8>>> options = {'max_function_evaluations': 5000,  # set optimizer options
 9...            'seed_rng': 2022,
10...            'mean': 3*numpy.ones((2,)),
11...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
12>>> ones = ONES(problem, options)  # initialize the optimizer class
13>>> results = ones.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"ONES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16ONES: 5000, 4.08973753355584e-05
lr_mean

learning rate of distribution mean update (should > 0.0).

Type:

float

lr_sigma

learning rate of global step-size adaptation (should > 0.0).

Type:

float

mean

initial (starting) point, aka mean of Gaussian search/sampling/mutation distribution. If not given, it will draw a random sample from the uniform distribution whose search range is bounded by problem[‘lower_boundary’] and problem[‘upper_boundary’], by default.

Type:

array_like

n_individuals

number of offspring/descendants, aka offspring population size (should > 0).

Type:

int

n_parents

number of parents/ancestors, aka parental population size (should > 0).

Type:

int

References

Beyer, H.G., 2023, July. What you always wanted to know about evolution strategies, but never dared to ask. In Proceedings of Companion Conference on Genetic and Evolutionary Computation (pp. 878-894). ACM.

Beyer, H.G., 2014. Convergence analysis of evolutionary algorithms that are based on the paradigm of information geometry. Evolutionary Computation, 22(4), pp.679-709.

Wierstra, D., Schaul, T., Glasmachers, T., Sun, Y., Peters, J. and Schmidhuber, J., 2014. Natural evolution strategies. Journal of Machine Learning Research, 15(1), pp.949-980.

Schaul, T., 2011. Studies in continuous black-box optimization. Doctoral Dissertation, Technische Universität München.

Please refer to the official Python source code from PyBrain (now not actively maintained): https://github.com/pybrain/pybrain/blob/master/pybrain/optimization/distributionbased/nes.py