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.

In this work, we provide an extended discussion of a new approach to explainable Reinforcement Learning called Diverse Near-Optimal Alternatives (DNA), first proposed at L4DC 2025. DNA seeks a set of reasonable "options" for trajectory-planning agents, optimizing policies to produce qualitatively diverse trajectories in Euclidean space. In the spirit of explainability, these distinct policies are used to "explain" an agent's options in terms of available trajectory shapes from which a human user may choose. In particular, DNA applies to value function-based policies on Markov decision processes where agents are limited to continuous trajectories. Here, we describe DNA, which uses reward shaping in local, modified Q-learning problems to solve for distinct policies with guaranteed epsilon-optimality. We show that it successfully returns qualitatively different policies that constitute meaningfully different "options" in simulation, including a brief comparison to related approaches in the stochastic optimization field of Quality Diversity. Beyond the explanatory motivation, this work opens new possibilities for exploration and adaptive planning in RL.

Quality Diversity (QD) has shown great success in discovering high-performing, diverse policies for robot skill learning. While current benchmarks have led to the development of powerful QD methods, we argue that new paradigms must be developed to facilitate open-ended search and generalizability. In particular, many methods focus on learning diverse agents that each move to a different xy position in MAP-Elites-style bounded archives. Here, we show that such tasks can be accomplished with a single, goal-conditioned policy paired with a classical planner, achieving O(1) space complexity w.r.t. the number of policies and generalization to task variants. We hypothesize that this approach is successful because it extracts task-invariant structural knowledge by modeling a relational graph between adjacent cells in the archive. We motivate this view with emerging evidence from computational neuroscience and explore connections between QD and models of cognitive maps in human and other animal brains. We conclude with a discussion exploring the relationships between QD and cognitive maps, and propose future research directions inspired by cognitive maps towards future generalizable algorithms capable of truly open-ended search.

Quality-Diversity (QD) methods are algorithms that aim to generate a set of diverse and high-performing solutions to a given problem. Originally developed for evolutionary robotics, most QD studies are conducted on a limited set of domains - mainly applied to locomotion, where the fitness and the behavior signal are dense. Grasping is a crucial task for manipulation in robotics. Despite the efforts of many research communities, this task is yet to be solved. Grasping cumulates unprecedented challenges in QD literature: it suffers from reward sparsity, behavioral sparsity, and behavior space misalignment. The present work studies how QD can address grasping. Experiments have been conducted on 15 different methods on 10 grasping domains, corresponding to 2 different robot-gripper setups and 5 standard objects. An evaluation framework that distinguishes the evaluation of an algorithm from its internal components has also been proposed for a fair comparison. The obtained results show that MAP-Elites variants that select successful solutions in priority outperform all the compared methods on the studied metrics by a large margin. We also found experimental evidence that sparse interaction can lead to deceptive novelty. To our knowledge, the ability to efficiently produce examples of grasping trajectories demonstrated in this work has no precedent in the literature.

Minecraft is a great testbed for human creativity that has inspired the design of various structures and even functioning machines, including flying machines. EvoCraft is an API for programmatically generating structures in Minecraft, but the initial work in this domain was not capable of evolving flying machines. This paper applies fitness-based evolution and quality diversity search in order to evolve flying machines. Although fitness alone can occasionally produce flying machines, thanks in part to a more sophisticated fitness function than was used previously, the quality diversity algorithm MAP-Elites is capable of discovering flying machines much more reliably, at least when an appropriate behavior characterization is used to guide the search for diverse solutions.

In this work, we consider the problem of Quality-Diversity (QD) optimization with multiple objectives. 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. Thriving for diversity was shown to be useful in many industrial and robotics applications. On the other hand, most real-life problems exhibit several potentially antagonist objectives to be optimized. Hence being able to optimize for multiple objectives with an appropriate technique while thriving for diversity is important to many fields. Here, we propose an extension of the MAP-Elites algorithm in the multi-objective setting: Multi-Objective MAP-Elites (MOME). Namely, it combines the diversity inherited from the MAP-Elites grid algorithm with the strength of multi-objective optimizations by filling each cell with a Pareto Front. As such, it allows to extract diverse solutions in the descriptor space while exploring different compromises between objectives. We evaluate our method on several tasks, from standard optimization problems to robotics simulations. Our experimental evaluation shows the ability of MOME to provide diverse solutions while providing global performances similar to standard multi-objective algorithms.

One of the most important lessons from the success of deep learning is that learned representations tend to perform much better at any task compared to representations we design by hand. Yet evolution of evolvability algorithms, which aim to automatically learn good genetic representations, have received relatively little attention, perhaps because of the large amount of computational power they require. The recent method Evolvability ES allows direct selection for evolvability with little computation. However, it can only be used to solve problems where evolvability and task performance are aligned. We propose Quality Evolvability ES, a method that simultaneously optimizes for task performance and evolvability and without this restriction. Our proposed approach Quality Evolvability has similar motivation to Quality Diversity algorithms, but with some important differences. While Quality Diversity aims to find an archive of diverse and well-performing, but potentially genetically distant individuals, Quality Evolvability aims to find a single individual with a diverse and well-performing distribution of offspring. By doing so Quality Evolvability is forced to discover more evolvable representations. We demonstrate on robotic locomotion control tasks that Quality Evolvability ES, similarly to Quality Diversity methods, can learn faster than objective-based methods and can handle deceptive problems.