mlsanityData to 14 Oct 2026

Differentiable Quality Diversity

arXiv 2106.03894 ↗First posted 7 Jun 2021cs.AIcited by 72

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Abstract (arXiv)

Quality diversity (QD) is a growing branch of stochastic optimization research that studies the problem of generating an archive of solutions that maximize a given objective function but are also diverse with respect to a set of specified measure functions. However, even when these functions are differentiable, QD algorithms treat them as "black boxes", ignoring gradient information. We present the differentiable quality diversity (DQD) problem, a special case of QD, where both the objective and measure functions are first order differentiable. We then present MAP-Elites via a Gradient Arborescence (MEGA), a DQD algorithm that leverages gradient information to efficiently explore the joint range of the objective and measure functions. Results in two QD benchmark domains and in searching the latent space of a StyleGAN show that MEGA significantly outperforms state-of-the-art QD algorithms, highlighting DQD's promise for efficient quality diversity optimization when gradient information is available. Source code is available at https://github.com/icaros-usc/dqd.

Key facts. Cited by 72 papers in the map (data through 14 Oct 2026). Builds on 38 of its 66 references that are in the map. First posted on arXiv 7 Jun 2021.

Builds on

38 of 66 references.

References · 38

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  3. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  4. 2015Illuminating search spaces by mapping elitescited by 425
  5. 2016The CMA Evolution Strategy: A Tutorialcited by 377
  6. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  7. 2020First return, then explorecited by 266
  8. 2019On the "steerability" of generative adversarial networkscited by 248
  9. 2014Robots that can adapt like animalscited by 204
  10. 2017Optimizing the Latent Space of Generative Networkscited by 157
  11. 2016COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Settingcited by 138
  12. 2020Effective Diversity in Population Based Reinforcement Learningcited by 119
26 more
  1. 2017Quality and Diversity Optimization: A Unifying Modular Frameworkcited by 113
  2. 2017Improving Exploration in Evolution Strategies for Deep Reinforcement Learning via a Population of Novelty-Seeking Agentscited by 107
  3. 2016Deep Feature Interpolation for Image Content Changescited by 80
  4. 2019Covariance Matrix Adaptation for the Rapid Illumination of Behavior Spacecited by 78
  5. 2018Evolving Mario Levels in the Latent Space of a Deep Convolutional Generative Adversarial Networkcited by 76
  6. 2016Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithmcited by 66
  7. 2020Quality-Diversity Optimization: a novel branch of stochastic optimizationcited by 60
  8. 2021Generating images from caption and vice versa via CLIP-Guided Generative Latent Space Searchcited by 57
  9. 2020Illuminating Mario Scenes in the Latent Space of a Generative Adversarial Networkcited by 52
  10. 2019AlphaStar: An Evolutionary Computation Perspectivecited by 50
  11. 2019The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learningcited by 46
  12. 2019Procedural Content Generation through Quality Diversitycited by 45
  13. 2018Discovering the Elite Hypervolume by Leveraging Interspecies Correlationcited by 41
  14. 2018Data-Efficient Design Exploration through Surrogate-Assisted Illuminationcited by 38
  15. 2020Scaling MAP-Elites to Deep Neuroevolutioncited by 38
  16. 2019Mapping Hearthstone Deck Spaces through MAP-Elites with Sliding Boundariescited by 32
  17. 2021Generating and Blending Game Levels via Quality-Diversity in the Latent Space of a Variational Autoencodercited by 27
  18. 2020A Quality Diversity Approach to Automatically Generating Human-Robot Interaction Scenarios in Shared Autonomycited by 20
  19. 2021Policy Manifold Search: Exploring the Manifold Hypothesis for Diversity-based Neuroevolutioncited by 20
  20. 2020CPPN2GAN: Combining Compositional Pattern Producing Networks and GANs for Large-scale Pattern Generationcited by 19
  21. 2020BOP-Elites, a Bayesian Optimisation algorithm for Quality-Diversity searchcited by 15
  22. 2021Illuminating the Space of Beatable Lode Runner Levels Produced By Various Generative Adversarial Networkscited by 14
  23. 2020Fast and stable MAP-Elites in noisy domains using deep gridscited by 13
  24. 2021Monte Carlo Elites: Quality-Diversity Selection as a Multi-Armed Bandit Problemcited by 10
  25. 2020The Hessian Estimation Evolution Strategycited by 2
  26. 2020Discovering Representations for Black-box Optimizationcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 14; 2023: 23; 2024: 15; 2025: 8; 2026: 10.

72 papers.

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  1. 2023Large Language Models Suffer From Their Own Output: An Analysis of the Self-Consuming Training Loopcited by 79
  2. 2022Deep Surrogate Assisted Generation of Environmentscited by 40
  3. 2022Approximating Gradients for Differentiable Quality Diversity in Reinforcement Learningcited by 38
  4. 2021On the Importance of Environments in Human-Robot Coordinationcited by 37
  5. 2021Illuminating Diverse Neural Cellular Automata for Level Generationcited by 35
  6. 2023pyribs: A Bare-Bones Python Library for Quality Diversity Optimizationcited by 30
  7. 2024Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey on Hybrid Algorithmscited by 26
  8. 2022Covariance Matrix Adaptation MAP-Annealingcited by 25
  9. 2023Proximal Policy Gradient Arborescence for Quality Diversity Reinforcement Learningcited by 20
  10. 2022Multi-Objective Quality Diversity Optimizationcited by 19
  11. 2022On the Versatile Uses of Partial Distance Correlation in Deep Learningcited by 19
  12. 2023Generating Behaviorally Diverse Policies with Latent Diffusion Modelscited by 19
38 more
  1. 2023QDax: A Library for Quality-Diversity and Population-based Algorithms with Hardware Accelerationcited by 17
  2. 2022Accelerated Quality-Diversity through Massive Parallelismcited by 14
  3. 2022ERL-Re2: Efficient Evolutionary Reinforcement Learning with Shared State Representation and Individual Policy Representationcited by 14
  4. 2026KernelFoundry: Hardware-aware evolutionary GPU kernel optimizationcited by 13
  5. 2024CaDRE: Controllable and Diverse Generation of Safety-Critical Driving Scenarios using Real-World Trajectoriescited by 11
  6. 2022COIL: Constrained Optimization in Learned Latent Space: Learning Representations for Valid Solutionscited by 10
  7. 2022Training Diverse High-Dimensional Controllers by Scaling Covariance Matrix Adaptation MAP-Annealingcited by 10
  8. 2022Benchmarking Quality-Diversity Algorithms on Neuroevolution for Reinforcement Learningcited by 10
  9. 2023Quality Diversity through Human Feedback: Towards Open-Ended Diversity-Driven Optimizationcited by 10
  10. 2023Arbitrarily Scalable Environment Generators via Neural Cellular Automatacited by 9
  11. 2025Quality-Diversity Red-Teaming: Automated Generation of High-Quality and Diverse Attackers for Large Language Modelscited by 9
  12. 2022Relevance-guided Unsupervised Discovery of Abilities with Quality-Diversity Algorithmscited by 8
  13. 2023Surrogate Assisted Generation of Human-Robot Interaction Scenarioscited by 8
  14. 2024Large Language Models as In-context AI Generators for Quality-Diversitycited by 7
  15. 2023Quality Diversity under Sparse Reward and Sparse Interaction: Application to Grasping in Roboticscited by 6
  16. 2023Synergizing Quality-Diversity with Descriptor-Conditioned Reinforcement Learningcited by 6
  17. 2023Evolving Populations of Diverse RL Agents with MAP-Elitescited by 5
  18. 2023Who Needs to Know? Minimal Knowledge for Optimal Coordinationcited by 5
  19. 2023Diversity from Human Feedbackcited by 5
  20. 2023Keep Various Trajectories: Promoting Exploration of Ensemble Policies in Continuous Controlcited by 5
  21. 2024Multi-Objective Quality-Diversity for Crystal Structure Predictioncited by 5
  22. 2022How to Fill the Optimum Set? Population Gradient Descent with Harmless Diversitycited by 4
  23. 2023Leveraging Human Feedback to Evolve and Discover Novel Emergent Behaviors in Robot Swarmscited by 4
  24. 2023Gradient-Informed Quality Diversity for the Illumination of Discrete Spacescited by 4
  25. 2024Parametric-Task MAP-Elitescited by 4
  26. 2024Diversifying Policy Behaviors with Extrinsic Behavioral Curiositycited by 4
  27. 2024Imitation from Diverse Behaviors: Wasserstein Quality Diversity Imitation Learning with Single-Step Archive Explorationcited by 4
  28. 2022A Collection of Quality Diversity Optimization Problems Derived from Hyperparameter Optimization of Machine Learning Modelscited by 3
  29. 2023Don't Bet on Luck Alone: Enhancing Behavioral Reproducibility of Quality-Diversity Solutions in Uncertain Domainscited by 3
  30. 2023CHSEL: Producing Diverse Plausible Pose Estimates from Contact and Free Space Datacited by 3
  31. 2024Enabling Adaptive Agent Training in Open-Ended Simulators by Targeting Diversitycited by 3
  32. 2025Improving Human-AI Coordination through Online Adversarial Training and Generative Modelscited by 3
  33. 2025AutoQD: Automatic Discovery of Diverse Behaviors with Quality-Diversity Optimizationcited by 3
  34. 2023Improving the Data Efficiency of Multi-Objective Quality-Diversity through Gradient Assistance and Crowding Explorationcited by 2
  35. 2023Enhancing MAP-Elites with Multiple Parallel Evolution Strategiescited by 2
  36. 2023Enhancing the Hierarchical Environment Design via Generative Trajectory Modelingcited by 2
  37. 2023Density Descent for Diversity Optimizationcited by 2
  38. 2025MUSS: Multilevel Subset Selection for Relevance and Diversitycited by 2

50 most cited of 72 All 72 (JSON)