Discount Model Search for Quality Diversity Optimization in High-Dimensional Measure Spaces

This repository is the implementation of Discount Model Search for Quality Diversity Optimization in High-Dimensional Measure Spaces by Bryon Tjanaka, Henry Chen, Matthew C. Fontaine, and Stefanos Nikolaidis.

Installation

uv sync

# For StyleGAN3.
git clone https://github.com/NVlabs/stylegan3.git
curl -L 'https://api.ngc.nvidia.com/v2/models/org/nvidia/team/research/stylegan3/1/files?redirect=true&path=stylegan3-t-ffhqu-256x256.pkl' -o 'stylegan3-t-ffhqu-256x256.pkl'

If running in the LSI (Hiker) domain, download the LHQ256 dataset from here. Place the dataset in the lhq_256_root/ directory, such that the directory structure looks like this:

lhq_256_root
└── lhq_256
    ├── 0000000.png
    ├── 0000001.png
    ├── 0000002.png
    ├── 0000003.png
    ...

Generating Centroids

We have already generated centroids and stored them in this repo under src/cvt/centroids/. However, new centroids can be generated as follows. Place any generated files under src/cvt/centroids/, or modify the centroids path in the configs in config/algo/archive/.

1. 10D, 20D, and 50D LP domains:

   # 10D
   uv run -m src.cvt.make_centroids \
       domain=flat_multi_100d \
       +centroid_cells=10000 \
       +centroid_file=src/cvt/centroids/flat_multi_100d.npy
   
   # 20D
   uv run -m src.cvt.make_centroids \
       domain=sphere_20_100d \
       +centroid_cells=10000 \
       +centroid_file=src/cvt/centroids/sphere_20_100d.npy
   
   # 50D
   uv run -m src.cvt.make_centroids \
       domain=sphere_50_100d \
       +centroid_cells=10000 \
       +centroid_file=src/cvt/centroids/sphere_50_100d.npy

2. TA (MNIST):

   uv run -m src.cvt.mnist_centroids

3. TA (F-MNIST):

   uv run -m src.cvt.fashion_mnist_centroids

4. LSI (Hiker): Make sure to download the LHQ256 dataset as described above. Then:

   uv run -m src.cvt.lhq_centroids

Experiments

The following commands will run DMS and all baselines for the paper in all domains. Note that we use the following names for the domains in the paper:

Name in Paper	Name in Code
2D LP (Sphere)	sphere_100d
10D LP (Sphere)	sphere_multi_100d
20D LP (Sphere)	sphere_20_100d
50D LP (Sphere)	sphere_50_100d
2D LP (Rastrigin)	rastrigin_100d
10D LP (Rastrigin)	rastrigin_multi_100d
2D LP (Flat)	flat_100d
10D LP (Flat)	flat_multi_100d
Arm Repertoire	arm_100d
TA (MNIST)	triangles_mnist
TA (F-MNIST)	triangles_fashion_mnist
LSI (Hiker)	lsi_face

# DMS -- for the benchmark domains, we include commands to run all ablations in
# the paper, i.e., learning rate, restart rule, and number of empty points.
bash scripts/paper/dms_100d.sh sphere_100d lr
bash scripts/paper/dms_100d.sh sphere_100d restart_100
bash scripts/paper/dms_100d.sh sphere_100d n_empty
bash scripts/paper/dms_multi_100d.sh sphere_multi_100d lr
bash scripts/paper/dms_multi_100d.sh sphere_multi_100d restart_basic
bash scripts/paper/dms_multi_100d.sh sphere_multi_100d n_empty
bash scripts/paper/dms_20_100d.sh sphere_20_100d default
bash scripts/paper/dms_50_100d.sh sphere_50_100d default
bash scripts/paper/dms_100d.sh rastrigin_100d lr
bash scripts/paper/dms_100d.sh rastrigin_100d restart_100
bash scripts/paper/dms_100d.sh rastrigin_100d n_empty
bash scripts/paper/dms_multi_100d.sh rastrigin_multi_100d lr
bash scripts/paper/dms_multi_100d.sh rastrigin_multi_100d restart_basic
bash scripts/paper/dms_multi_100d.sh rastrigin_multi_100d n_empty
bash scripts/paper/dms_100d.sh flat_100d lr
bash scripts/paper/dms_100d.sh flat_100d restart_100
bash scripts/paper/dms_100d.sh flat_100d n_empty
bash scripts/paper/dms_multi_100d.sh flat_multi_100d lr
bash scripts/paper/dms_multi_100d.sh flat_multi_100d restart_basic
bash scripts/paper/dms_multi_100d.sh flat_multi_100d n_empty
bash scripts/paper/dms_100d.sh arm_100d lr
bash scripts/paper/dms_100d.sh arm_100d restart_100
bash scripts/paper/dms_100d.sh arm_100d n_empty
bash scripts/paper/dms_triangles_mnist.sh triangles_mnist
bash scripts/paper/dms_triangles_mnist.sh triangles_fashion_mnist
bash scripts/paper/dms_lsi_face.sh

# CMA-MAE
bash scripts/paper/cma_mae_100d.sh sphere_100d
bash scripts/paper/cma_mae_multi_100d.sh sphere_multi_100d
bash scripts/paper/cma_mae_20_100d.sh sphere_20_100d
bash scripts/paper/cma_mae_50_100d.sh sphere_50_100d
bash scripts/paper/cma_mae_100d.sh rastrigin_100d
bash scripts/paper/cma_mae_multi_100d.sh rastrigin_multi_100d
bash scripts/paper/cma_mae_100d.sh flat_100d
bash scripts/paper/cma_mae_multi_100d.sh flat_multi_100d
bash scripts/paper/cma_mae_100d.sh flat_100d
bash scripts/paper/cma_mae_triangles_mnist.sh triangles_mnist
bash scripts/paper/cma_mae_triangles_mnist.sh triangles_fashion_mnist
bash scripts/paper/cma_mae_lsi_face.sh

# DDS
bash scripts/paper/dds_100d.sh sphere_100d
bash scripts/paper/dds_multi_100d.sh sphere_multi_100d
bash scripts/paper/dds_20_100d.sh sphere_20_100d
bash scripts/paper/dds_50_100d.sh sphere_50_100d
bash scripts/paper/dds_100d.sh rastrigin_100d
bash scripts/paper/dds_multi_100d.sh rastrigin_multi_100d
bash scripts/paper/dds_100d.sh flat_100d
bash scripts/paper/dds_multi_100d.sh flat_multi_100d
bash scripts/paper/dds_100d.sh arm_100d

# MAP-Elites (line)
bash scripts/paper/map_elites_line_100d.sh sphere_100d
bash scripts/paper/map_elites_line_multi_100d.sh sphere_multi_100d
bash scripts/paper/map_elites_line_20_100d.sh sphere_20_100d
bash scripts/paper/map_elites_line_50_100d.sh sphere_50_100d
bash scripts/paper/map_elites_line_100d.sh rastrigin_100d
bash scripts/paper/map_elites_line_multi_100d.sh rastrigin_multi_100d
bash scripts/paper/map_elites_line_100d.sh flat_100d
bash scripts/paper/map_elites_line_multi_100d.sh flat_multi_100d
bash scripts/paper/map_elites_line_100d.sh arm_100d
bash scripts/paper/map_elites_line_triangles_mnist.sh triangles_mnist
bash scripts/paper/map_elites_line_triangles_mnist.sh triangles_fashion_mnist
bash scripts/paper/map_elites_line_lsi_face.sh

# MAP-Elites
bash scripts/paper/map_elites_100d.sh sphere_100d
bash scripts/paper/map_elites_multi_100d.sh sphere_multi_100d
bash scripts/paper/map_elites_20_100d.sh sphere_20_100d
bash scripts/paper/map_elites_50_100d.sh sphere_50_100d
bash scripts/paper/map_elites_100d.sh rastrigin_100d
bash scripts/paper/map_elites_multi_100d.sh rastrigin_multi_100d
bash scripts/paper/map_elites_100d.sh flat_100d
bash scripts/paper/map_elites_multi_100d.sh flat_multi_100d
bash scripts/paper/map_elites_100d.sh arm_100d
bash scripts/paper/map_elites_triangles_mnist.sh triangles_mnist
bash scripts/paper/map_elites_triangles_mnist.sh triangles_fashion_mnist
bash scripts/paper/map_elites_lsi_face.sh

Analysis

Running the experiments above will produce logging directories under the logs/ directory, e.g., logs/dms_arm_100d_lr/. If desired, move the results into a new results/ directory, and in that directory, create a manifest.yaml listing out the directories -- refer to analysis/src/analysis/figures.py for the format of this manifest.

Follow the instructions in analysis/README.md for generating plots with the given manifest. Note that the analysis code uses different dependencies from the main repo.

Citation

@misc{tjanaka2026discountmodelsearchquality,
      title={Discount Model Search for Quality Diversity Optimization in High-Dimensional Measure Spaces},
      author={Bryon Tjanaka and Henry Chen and Matthew C. Fontaine and Stefanos Nikolaidis},
      year={2026},
      eprint={2601.01082},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2601.01082},
}