Global Optimization through High-Resolution Sampling

This package provides functions to run a global optimization algorithm, specifically designed to explore the properties of high-dimensional functions through High-Resolution sampling, based on [1]. The package includes tools for defining functions, setting optimization parameters, generating samples, and visualizing empirical probabilities.

Installation

The package is available through pip, and may be installed via:

pip install GlobalOptimizationHRLA

If running the package locally, you can install it using:

pip install .

Setup

In order to use this package, you need to define:

• The target function and its gradient.
• An initial distribution for the search space.

Main Usage

1. Defining the Target Function and Gradient

The provided example uses the Rastrigin function as the target for optimization.

import numpy as np

d = 10
U = lambda x: d + np.linalg.norm(x) ** 2 - np.sum(np.cos(2 * np.pi * x))
dU = lambda x: 2 * x + 2 * np.pi * np.sin(2 * np.pi * x)

2. Sampling from an Initial Distribution

Define an initial distribution from which samples are generated:

initial = lambda: np.random.multivariate_normal(np.zeros(d) + 3, 10 * np.eye(d))

3. Running the Algorithm

To execute the global optimization algorithm, use the DNLA.Algorithm class.

import GlobalOptimizationHRLA as HRLA

algorithm = HRLA.Algorithm(d=d, M=100, N=10, K=14000, h=0.01, title=title, U=U, dU=dU, initial=initial)
samples_filename = algorithm.generate_samples(As=[1,2,3,4], sim_annealing=False)

Parameters:

• d (int): Dimension of the search space.
• M (int): Number of particles in the swarm.
• N (int): Number of generations for resampling.
• K (int): Total number of iterations to perform.
• h (float): Step size for gradient descent.
• title (str): Title for the optimization, useful for organizing saved data.
• U (function): The target function to optimize.
• dU (function): The gradient of the target function.
• initial (function): The initial distribution for generating particles.
• As (list): List of tolerances or annealing factors to adjust optimization.
• sim_annealing (bool): Determines whether to apply simulated annealing (default is False).

Returns:

• samples_filename (str): Path to the file where generated samples are saved.

Examples

Examples may in found in the /tests directory of the repository. Postprocessing tools are detailed in /tests/PostProcessing/README.md

References

[1] Cortild, D., Delplancke, C., Oudjane, N., & Peypouquet, J. (2025). Global Optimization Algorithm through High-Resolution Sampling. Transactions on Machine Learning Research, Sep 2025. https://openreview.net/forum?id=r3VEA1AWY5