CMA-ES with Learning Rate Adaptation (GECCO2023 Best Paper Nominatation [slide] and ACM TELO)

About

This repository contains the code for the paper "CMA-ES with Learning Rate Adaptation: Can CMA-ES with Default Population Size Solve Multimodal and Noisy Problems?" by Masahiro Nomura, Youhei Akimoto, and Isao Ono, which has been accepted to GECCO'23 (Best Paper Nominated at ENUM Track). The extended version of this paper, "CMA-ES with Learning Rate Adaptation" is accepted for ACM Transactions on Evolutionary Learning.

You can also use the LRA-CMA-ES via the following Python libraries:

• cmaes (Recommended): It's only necessary to specify lr_adapt=True when using CMA.
• Optuna: Similarly, it's only necessary to specify lr_adapt=True in CmaEsSampler.

If you find this code useful in your research then please cite:

@inproceedings{nomura2023cma,
author = {Nomura, Masahiro and Akimoto, Youhei and Ono, Isao},
title = {CMA-ES with Learning Rate Adaptation: Can CMA-ES with Default Population Size Solve Multimodal and Noisy Problems?},
year = {2023},
isbn = {9798400701191},
publisher = {Association for Computing Machinery},
url = {https://doi.org/10.1145/3583131.3590358},
doi = {10.1145/3583131.3590358},
booktitle = {Proceedings of the Genetic and Evolutionary Computation Conference},
pages = {839–847},
numpages = {9},
location = {Lisbon, Portugal},
series = {GECCO '23}
}

@article{nomura2024cma,
  title={CMA-ES with Learning Rate Adaptation},
  author={Nomura, Masahiro and Akimoto, Youhei and Ono, Isao},
  journal={ACM Transactions on Evolutionary Learning},
  year={2024},
}

Dependencies

• numpy=1.24.2

Example (Noiseless)

In the noiseless case, e.g. Sphere function, you can run the code by the following command:

python main.py --function=sphere \
  --dim=10 \
  --mean=3.0 \
  --sigma=2.0

Users can specify the experimental settings by adding the following flags:

• --function: objective function (required; please see the below)
• --dim: # dimension (required)
• --mean: initial mean vector (required; currently only scalar value is accepted)
• --sigma: initial step-size (required)
• --max_evals: maximum # evaluations (default=10000000; int)
• --criterion: target value, i.e., the optimization will stop when the function value reaches it (default=1e-3; float)

You can run the experiments on other functions by specifying such arguments in the same way. The benchmark functions include sphere (Sphere), ellipsoid (Ellipsoid), rosen (Rosenbrock), ackley (Ackley), schaffer (Schaffer), rastrigin (Rastrigin), bohachevsky (Bohachevsky), and griewank (Griewank),

Example (Noisy)

In the noiseless case, e.g. NoisySphere function with variance=1.0, you can run the code by the following command:

python main.py --function=noisysphere-var=1.0 \
  --dim=10 \
  --mean=3.0 \
  --sigma=2.0

You can specify the variance by changing the 1.0 in the noisysphere-var=1.0. The benchmark functions include noisysphere-var=... (NoisySphere), noisyellipsoid-var=... (NoisyEllipsoid), and noisyrastrigin-var=... (NoisyRastrigin).