Support CMA-ES with Margin.

[knshnb]

The implementation of CMA-ES with margin by #115 has the following issues.

• It is implicit that discrete spaces must be located at the latter dimensions.
• The argument of __init__ is inconsistent with CMA.

This PR is a continuation of #115 and changes the interface of CMAwM to address the issues. The example code would be changed as follows.

import numpy as np
from cmaes import CMAwM


def ellipsoid_onemax(x, n_zdim):
    n = len(x)
    n_rdim = n - n_zdim
    r = 10
    if len(x) < 2:
        raise ValueError("dimension must be greater one")
    ellipsoid = sum([(1000 ** (i / (n_rdim - 1)) * x[i]) ** 2 for i in range(n_rdim)])
    onemax = n_zdim - (0.0 < x[(n - n_zdim) :]).sum()
    return ellipsoid + r * onemax


def main():
    binary_dim, continuous_dim = 10, 10
    dim = binary_dim + continuous_dim
    bounds = np.concatenate(
        [
            np.tile([0, 1], (binary_dim, 1)),
            np.tile([-np.inf, np.inf], (continuous_dim, 1)),
        ]
    )
    steps = np.concatenate([np.ones(binary_dim), np.zeros(continuous_dim)])
    optimizer = CMAwM(mean=np.zeros(dim), sigma=2.0, bounds=bounds, steps=steps)
    print(" evals    f(x)")
    print("======  ==========")

    evals = 0
    while True:
        solutions = []
        for _ in range(optimizer.population_size):
            x_for_eval, x_for_tell = optimizer.ask()
            value = ellipsoid_onemax(x_for_eval, binary_dim)
            evals += 1
            solutions.append((x_for_tell, value))
            if evals % 300 == 0:
                print(f"{evals:5d}  {value:10.5f}")
        optimizer.tell(solutions)

        if optimizer.should_stop():
            break


if __name__ == "__main__":
    main()

[c-bata]

Thank you for your pull request!

@nomuramasahir0 Could you trigger the GitHub action on this PR?

[c-bata]

I opened #122 to fix CI problems 🙇

[c-bata]

Changes overall looks good to me and the current interface looks more straightforward than #115.
We might want to consider refactoring duplicated code with CMA class, but as for this change, the current implementation looks good to me. We can work on it as follow-up tasks.

I left two minor comments.

[c-bata]

Should we add scipy in extra_requires?

[knshnb]

I added cmawm = scipy. ( b3a9608)

[knshnb]

Thanks for the review! I applied your comments.

I'm sorry for the PR with a large change. Please see cmaes/_cmawm.py and examples/cmaes_with_margin.py in https://github.com/CyberAgentAILab/cmaes/compare/3938dee69ebb707cf68ad7aaebd299001dec0ce7..1ef697199592f2e2433fa3648c95ff3d24afd3b5 for the main change from #115.

Although the behavior with the same seed is different from #115 (because I changed the order of internal representations), I checked that we can obtain similar tendencies in benchmark problems. 2000 trials, 100 runs for each sampler in each problem:

(_CmaEsSampler_NopPruner_0: Original, _CmaEsSampler_NopPruner_1: CMA-ES with margin)

[c-bata]

Thanks for the update! LGTM!