# Gradient-Informed Quality Diversity for the Illumination of Discrete Spaces

arXiv: https://arxiv.org/abs/2306.05138 · HTML: https://mlsanity.com/paper/2306.05138/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 8 Jun 2023.

## Builds on (most cited first, 24 of 24)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Make-A-Scene: Scene-Based Text-to-Image Generation with Human Priors](https://mlsanity.com/paper/2203.13131/) (2022)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Discrete Variational Autoencoders](https://mlsanity.com/paper/1609.02200/) (2016)
- [Quality and Diversity Optimization: A Unifying Modular Framework](https://mlsanity.com/paper/1708.09251/) (2017)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space](https://mlsanity.com/paper/1912.02400/) (2019)
- [Differentiable Quality Diversity](https://mlsanity.com/paper/2106.03894/) (2021)
- [Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm](https://mlsanity.com/paper/1610.05729/) (2016)
- [Quality-Diversity Optimization: a novel branch of stochastic optimization](https://mlsanity.com/paper/2012.04322/) (2020)
- [Autonomous skill discovery with Quality-Diversity and Unsupervised Descriptors](https://mlsanity.com/paper/1905.11874/) (2019)
- [Diversity Policy Gradient for Sample Efficient Quality-Diversity Optimization](https://mlsanity.com/paper/2006.08505/) (2020)
- [Illuminating Mario Scenes in the Latent Space of a Generative Adversarial Network](https://mlsanity.com/paper/2007.05674/) (2020)
- [AlphaStar: An Evolutionary Computation Perspective](https://mlsanity.com/paper/1902.01724/) (2019)
- [Discovering the Elite Hypervolume by Leveraging Interspecies Correlation](https://mlsanity.com/paper/1804.03906/) (2018)
- [CPPN2GAN: Combining Compositional Pattern Producing Networks and GANs for Large-scale Pattern Generation](https://mlsanity.com/paper/2004.01703/) (2020)
- [Multi-Objective Quality Diversity Optimization](https://mlsanity.com/paper/2202.03057/) (2022)
- [Fast and stable MAP-Elites in noisy domains using deep grids](https://mlsanity.com/paper/2006.14253/) (2020)

## Built on by (most cited first, 4 of 4)

- [AutoQD: Automatic Discovery of Diverse Behaviors with Quality-Diversity Optimization](https://mlsanity.com/paper/2506.05634/) (2025)
- [Preference-Conditioned Gradient Variations for Multi-Objective Quality-Diversity](https://mlsanity.com/paper/2411.12433/) (2024)
- [Soft Quality-Diversity Optimization](https://mlsanity.com/paper/2512.00810/) (2025)
- [Discount Model Search for Quality Diversity Optimization in High-Dimensional Measure Spaces](https://mlsanity.com/paper/2601.01082/) (2026)

## Abstract (arXiv)

Quality Diversity (QD) algorithms have been proposed to search for a large collection of both diverse and high-performing solutions instead of a single set of local optima. While early QD algorithms view the objective and descriptor functions as black-box functions, novel tools have been introduced to use gradient information to accelerate the search and improve overall performance of those algorithms over continuous input spaces. However a broad range of applications involve discrete spaces, such as drug discovery or image generation. Exploring those spaces is challenging as they are combinatorially large and gradients cannot be used in the same manner as in continuous spaces. We introduce map-elites with a Gradient-Informed Discrete Emitter (ME-GIDE), which extends QD optimisation with differentiable functions over discrete search spaces. ME-GIDE leverages the gradient information of the objective and descriptor functions with respect to its discrete inputs to propose gradient-informed updates that guide the search towards a diverse set of high quality solutions. We evaluate our method on challenging benchmarks including protein design and discrete latent space illumination and find that our method outperforms state-of-the-art QD algorithms in all benchmarks.