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-ofthe-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.

We study the problem of generating arbitrarily large environments to improve the throughput of multi-robot systems. Prior work proposes Quality Diversity (QD) algorithms as an effective method for optimizing the environments of automated warehouses. However, these approaches optimize only relatively small environments, falling short when it comes to replicating real-world warehouse sizes. The challenge arises from the exponential increase in the search space as the environment size increases.

We study the problem of generating arbitrarily large environments to improve the throughput of multi-robot systems. Prior work proposes Quality Diversity (QD) algorithms as an effective method for optimizing the environments of automated warehouses. However, these approaches optimize only relatively small environments, falling short when it comes to replicating real-world warehouse sizes. The challenge arises from the exponential increase in the search space as the environment size increases. Additionally, the previous methods have only been tested with up to 350 robots in simulations, while practical warehouses could host thousands of robots. In this paper, instead of optimizing environments, we propose to optimize Neural Cellular Automata (NCA) environment generators via QD algorithms. We train a collection of NCA generators with QD algorithms in small environments and then generate arbitrarily large environments from the generators at test time. We show that NCA environment generators maintain consistent, regularized patterns regardless of environment size, significantly enhancing the scalability of multi-robot systems in two different domains with up to 2,350 robots. Additionally, we demonstrate that our method scales a single-agent reinforcement learning policy to arbitrarily large environments with similar patterns.

Quality-Diversity algorithms have transformed optimization by prioritizing the discovery of diverse, high-performing solutions over a single optimal result. However, traditional Quality-Diversity methods, such as MAP-Elites, rely heavily on predefined behavior descriptors and complete prior knowledge of the task to define the behavior space grid, limiting their flexibility and applicability. In this work, we introduce Vector Quantized-Elites (VQ-Elites), a novel Quality-Diversity algorithm that autonomously constructs a structured behavior space grid using unsupervised learning, eliminating the need for prior task-specific knowledge. At the core of VQ-Elites is the integration of Vector Quantized Variational Autoencoders, which enables the dynamic learning of behavior descriptors and the generation of a structured, rather than unstructured, behavior space grid -- a significant advancement over existing unsupervised Quality-Diversity approaches. This design establishes VQ-Elites as a flexible, robust, and task-agnostic optimization framework. To further enhance the performance of unsupervised Quality-Diversity algorithms, we introduce behavior space bounding and cooperation mechanisms, which significantly improve convergence and performance, as well as the Effective Diversity Ratio and Coverage Diversity Score, two novel metrics that quantify the actual diversity in the unsupervised setting. We validate VQ-Elites on robotic arm pose-reaching, mobile robot space-covering, and MiniGrid exploration tasks. The results demonstrate its ability to efficiently generate diverse, high-quality solutions, emphasizing its adaptability, scalability, robustness to hyperparameters, and potential to extend Quality-Diversity optimization to complex, previously inaccessible domains.

Recent progress in legged robotics [1]-[4], particularly through the use of reinforcement learning (RL), has led to significant improvements in their performance in navigating complex terrains. However, despite these advances, significant challenges remain in ensuring the robustness of such systems, particularly when navigating unstructured terrains. Traversing unstructured terrains is crucial in applications that require the exploration of hazardous areas, such as rescue operations or underground inspections. Many studies rely on hand-crafted terrains, such as stairs, slopes, and discrete obstacles, or employ uncontrollable noise or Perlin noise [4], [5] to generate them. While these methods allow for training and testing controllers on a variety of terrains, their scope is limited, and they do not ensure the controller's reliability across all possible terrains. Critical corner cases may be missed, and, given the diversity of terrains the robot might encounter, these cases can be difficult to identify, especially as weaknesses can differ widely depending on the controller's design. Moreover, such weaknesses are often difficult to discover manually. In [6], 100 volunteers were asked to identify weaknesses in a quadruped robot's controller by applying pushing forces and overwriting velocity commands.

We study the problem of generating arbitrarily large environments to improve the throughput of multi-robot systems. Prior work proposes Quality Diversity (QD) algorithms as an effective method for optimizing the environments of automated warehouses. However, these approaches optimize only relatively small environments, falling short when it comes to replicating real-world warehouse sizes. The challenge arises from the exponential increase in the search space as the environment size increases.

Quality-Diversity has emerged as a powerful family of evolutionary algorithms that generate diverse populations of high-performing solutions by implementing local competition principles inspired by biological evolution. While these algorithms successfully foster diversity and innovation, their specific mechanisms rely on heuristics, such as grid-based competition in MAP-Elites or nearest-neighbor competition in unstructured archives. In this work, we propose a fundamentally different approach: using meta-learning to automatically discover novel Quality-Diversity algorithms. By parameterizing the competition rules using attention-based neural architectures, we evolve new algorithms that capture complex relationships between individuals in the descriptor space. Our discovered algorithms demonstrate competitive or superior performance compared to established Quality-Diversity baselines while exhibiting strong generalization to higher dimensions, larger populations, and out-of-distribution domains like robot control. Notably, even when optimized solely for fitness, these algorithms naturally maintain diverse populations, suggesting meta-learning rediscovers that diversity is fundamental to effective optimization.

Quality-Diversity is a family of evolutionary algorithms that generate diverse, high-performing solutions through local competition principles inspired by natural evolution. While research has focused on improving specific aspects of Quality-Diversity algorithms, surprisingly little attention has been paid to investigating alternative formulations of local competition itself -- the core mechanism distinguishing Quality-Diversity from traditional evolutionary algorithms. Most approaches implement local competition through explicit collection mechanisms like fixed grids or unstructured archives, imposing artificial constraints that require predefined bounds or hard-to-tune parameters. We show that Quality-Diversity methods can be reformulated as Genetic Algorithms where local competition occurs through fitness transformations rather than explicit collection mechanisms. Building on this insight, we introduce Dominated Novelty Search, a Quality-Diversity algorithm that implements local competition through dynamic fitness transformations, eliminating the need for predefined bounds or parameters. Our experiments show that Dominated Novelty Search significantly outperforms existing approaches across standard Quality-Diversity benchmarks, while maintaining its advantage in challenging scenarios like high-dimensional and unsupervised spaces.