[Proposal] Support 1D search space in CMA-ES

[y0z]

Motivation

At the moment, cmaes does not support 1D search space.
However, based on my understanding, the CMA-ES algorithm can naturally handle 1D search space, so I want to support it.
It has also been observed that some users want to support this (optuna/optuna#5524).

In this PR, I support 1D search space in CMA-ES.

Description of Changes

• Change an assertion in _cma.py to ensure n_dim > 0 rather than n_dim > 1.

I confirmed that the code with the above change passes all tests and works fine in the following toy example.

import numpy as np
from cmaes import CMA

def quadratic(x1):
    return (x1 - 3) ** 2

if __name__ == "__main__":
    optimizer = CMA(mean=np.zeros(1), sigma=1.3)

    for generation in range(20):
        solutions = []
        for _ in range(optimizer.population_size):
            x = optimizer.ask()
            value = quadratic(x[0])
            solutions.append((x, value))
            print(f"#{generation} {value} (x1={x[0]})")
        optimizer.tell(solutions)

Output: It is confirmed that the search converges towards the optimum (x1 = 3).

#0 16.643669924292066 (x1=-1.0796654181797876)
#0 7.2004261524959166 (x1=0.3166390193460894)
#0 8.189839736380824 (x1=0.1382103962064533)
#0 12.497988920536582 (x1=-0.5352494849071942)
#1 7.179325689223134 (x1=0.3205736268329496)
#1 3.6146114323456273 (x1=1.0987868524687645)
#1 5.255710328044975 (x1=0.7074663954382319)
#1 10.095710257035286 (x1=-0.17737474293406053)
...
#18 6.963502924227799e-05 (x1=2.9916552394137232)
#18 0.002559389599251478 (x1=2.94940958984895)
#18 0.004124398005827681 (x1=3.0642214762040525)
#18 7.020158315938154e-05 (x1=2.991621361497273)
#19 0.0063421454828861525 (x1=3.0796375883793963)
#19 6.989768552220104e-05 (x1=2.991639516430122)
#19 0.0026858233887192963 (x1=2.948175069814622)
#19 0.0012593115389895819 (x1=3.0354867797776803)

[nomuramasahir0]

Thank you for the PR! As you mentioned, CMA-ES can be applied to 1-D problems (in this case, CMA-ES essentially reduces to ES), although I haven't empirically tested it yet. Some hyperparameters, like the learning rate, might need adjustment, so let's see how it performs.