# Covariance Matrix Adaptation MAP-Annealing

arXiv: https://arxiv.org/abs/2205.10752 · HTML: https://mlsanity.com/paper/2205.10752/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 91 references that are in the map.
- First posted on arXiv 22 May 2022.

## Builds on (most cited first, 30 of 57)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [VQGAN-CLIP: Open Domain Image Generation and Editing with Natural Language Guidance](https://mlsanity.com/paper/2204.08583/) (2022)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [CLIPDraw: Exploring Text-to-Drawing Synthesis through Language-Image Encoders](https://mlsanity.com/paper/2106.14843/) (2021)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Effective Diversity in Population Based Reinforcement Learning](https://mlsanity.com/paper/2002.00632/) (2020)
- [Quality and Diversity Optimization: A Unifying Modular Framework](https://mlsanity.com/paper/1708.09251/) (2017)
- [Improving Exploration in Evolution Strategies for Deep Reinforcement Learning via a Population of Novelty-Seeking Agents](https://mlsanity.com/paper/1712.06560/) (2017)
- [Generative Models as a Data Source for Multiview Representation Learning](https://mlsanity.com/paper/2106.05258/) (2021)
- [The Surprising Creativity of Digital Evolution: A Collection of Anecdotes from the Evolutionary Computation and Artificial Life Research Communities](https://mlsanity.com/paper/1803.03453/) (2018)
- [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)
- [This dataset does not exist: training models from generated images](https://mlsanity.com/paper/1911.02888/) (2019)
- [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)
- [Procedural Content Generation through Quality Diversity](https://mlsanity.com/paper/1907.04053/) (2019)
- [Discovering the Elite Hypervolume by Leveraging Interspecies Correlation](https://mlsanity.com/paper/1804.03906/) (2018)
- [Data-Efficient Design Exploration through Surrogate-Assisted Illumination](https://mlsanity.com/paper/1806.05865/) (2018)

## Built on by (most cited first, 25 of 25)

- [pyribs: A Bare-Bones Python Library for Quality Diversity Optimization](https://mlsanity.com/paper/2303.00191/) (2023)
- [Proximal Policy Gradient Arborescence for Quality Diversity Reinforcement Learning](https://mlsanity.com/paper/2305.13795/) (2023)
- [Quality-Diversity Actor-Critic: Learning High-Performing and Diverse Behaviors via Value and Successor Features Critics](https://mlsanity.com/paper/2403.09930/) (2024)
- [Training Diverse High-Dimensional Controllers by Scaling Covariance Matrix Adaptation MAP-Annealing](https://mlsanity.com/paper/2210.02622/) (2022)
- [Explainable Benchmarking for Iterative Optimization Heuristics](https://mlsanity.com/paper/2401.17842/) (2024)
- [Arbitrarily Scalable Environment Generators via Neural Cellular Automata](https://mlsanity.com/paper/2310.18622/) (2023)
- [Surrogate Assisted Generation of Human-Robot Interaction Scenarios](https://mlsanity.com/paper/2304.13787/) (2023)
- [Quality Diversity under Sparse Reward and Sparse Interaction: Application to Grasping in Robotics](https://mlsanity.com/paper/2308.05483/) (2023)
- [Synergizing Quality-Diversity with Descriptor-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2401.08632/) (2023)
- [Parametric-Task MAP-Elites](https://mlsanity.com/paper/2402.01275/) (2024)
- [Speeding up 6-DoF Grasp Sampling with Quality-Diversity](https://mlsanity.com/paper/2403.06173/) (2024)
- [Diversifying Policy Behaviors with Extrinsic Behavioral Curiosity](https://mlsanity.com/paper/2410.06151/) (2024)
- [Imitation from Diverse Behaviors: Wasserstein Quality Diversity Imitation Learning with Single-Step Archive Exploration](https://mlsanity.com/paper/2411.06965/) (2024)
- [AutoQD: Automatic Discovery of Diverse Behaviors with Quality-Diversity Optimization](https://mlsanity.com/paper/2506.05634/) (2025)
- [Density Descent for Diversity Optimization](https://mlsanity.com/paper/2312.11331/) (2023)
- [Algorithmic Scenario Generation as Quality Diversity Optimization](https://mlsanity.com/paper/2409.04711/) (2024)
- [Preference-Conditioned Gradient Variations for Multi-Objective Quality-Diversity](https://mlsanity.com/paper/2411.12433/) (2024)
- [Algorithmic Prompt Generation for Diverse Human-like Teaming and Communication with Large Language Models](https://mlsanity.com/paper/2504.03991/) (2025)
- [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)
- [Optimization of Edge Directions and Weights for Mixed Guidance Graphs in Lifelong Multi-Agent Path Finding](https://mlsanity.com/paper/2602.23468/) (2026)
- [Placeit! A Framework for Learning Robot Object Placement Skills](https://mlsanity.com/paper/2510.09267/) (2025)
- [Quality-Diversity Optimization as Multi-Objective Optimization](https://mlsanity.com/paper/2602.00478/) (2026)
- [Parameter-Efficient Neuroevolution for Diverse LLM Generation: Quality-Diversity Optimization via Prompt Embedding Evolution](https://mlsanity.com/paper/2605.09781/) (2026)
- [Uncovering the Generative Landscape of Diffusion Models: A Spectral-Guided Quality-Diversity Diffusion Framework](https://mlsanity.com/paper/2610.15724/) (2026)

## Abstract (arXiv)

Single-objective optimization algorithms search for the single highest-quality solution with respect to an objective. Quality diversity (QD) optimization algorithms, such as Covariance Matrix Adaptation MAP-Elites (CMA-ME), search for a collection of solutions that are both high-quality with respect to an objective and diverse with respect to specified measure functions. However, CMA-ME suffers from three major limitations highlighted by the QD community: prematurely abandoning the objective in favor of exploration, struggling to explore flat objectives, and having poor performance for low-resolution archives. We propose a new quality diversity algorithm, Covariance Matrix Adaptation MAP-Annealing (CMA-MAE), that addresses all three limitations. We provide theoretical justifications for the new algorithm with respect to each limitation. Our theory informs our experiments, which support the theory and show that CMA-MAE achieves state-of-the-art performance and robustness.