clegaspi / hypercube-sampler

Sampling from a hypercube with non-linear constraints

hypercube-sampler

Created by Christian Legaspi, September 2019.

Description

This package samples the feasible region (polytope) for a problem defined on a unit hypercube with non-linear constraints.

Approach

This package uses a random walk to explore the feasible region (i.e. the region that satisfies the constraints). From a valid starting point specified in the constraint definition file, the algorithm selects a direction uniformly at random and selects a magnitude for the step uniformly at random, either forward or backward, such that it stays within the feasible region. If no such step size exists, then a new direction is selected. Once a valid direction and step size is found, the algorithm steps to the new point and process is repeated.

The implementation was created to be conscious of memory. The sampler can be iterated so that points are generated on the fly instead of being stored. However, the sample(n) function does return a list with n points for convenience.

Additionally, if the constraint file does not supply a valid point within the feasible region, the sampler will attempt to find a valid point automatically.

Currently, the algorithm only searches for valid step sizes such that it does not step over any region along the selected direction that violates the constraints. This algorithm could be improved by considering step sizes which may step over those regions and consider all valid locations along that direction within the unit hypercube.

Installation

• Clone repository
• Create your favorite virtual environment with python 3.7 (I prefer conda, myself)
• Within the virtual environment and the repository root, run pip install --editable .

Running the sampler

This package features a command line interface. To run the sampler:

• Within your virtual environment, run sampler <in-file> <out-file> <n_samples>
• <in-file> is the path and name of a formatted constraint definition file
• <out-file> is the path and name of the output file
• <n_samples> is the number of points to find on the hypercube

Additionally the sampler can be used in a Python project via:

from hypercube_sampler.sampler import Sampler
sampler = Sampler.from_constraint_file('/path/to/constraint_file.txt')

# Get a set number of samples
samples = sampler.sample(100)

# Or get samples one at a time ad infinitum
for sample in sampler:
    my_processing_function(sample)