Quality-Diversity (QD) algorithms have exhibited promising results across many domains and applications. However, uncertainty in fitness and behaviour estimations of solutions remains a major challenge when QD is used in complex real-world applications. While several approaches have been proposed to improve the performance in uncertain applications, many fail to address a key challenge: determining how to prioritise solutions that perform consistently under uncertainty, in other words, solutions that are reproducible. Most prior methods improve fitness and reproducibility jointly, ignoring the possibility that they could be contradictory objectives. For example, in robotics, solutions may reliably walk at 90% of the maximum velocity in uncertain environments, while solutions that walk faster are also more prone to falling over. As this is a trade-off, neither one of these two solutions is “better" than the other. Thus, algorithms cannot intrinsically select one solution over the other, but can only enforce given preferences over these two contradictory objectives. In this paper, we formalise this problem as the performance-reproducibility trade-off for uncertain QD. We propose two new a-priori QD algorithms that find efficient solutions for given preferences over the trade-offs. We also propose an a-posteriori QD algorithm for when these preferences cannot be defined in advance. Our results show that our approaches successfully find solutions that satisfy given preferences. Importantly, by simply accounting for this trade-off, our approaches perform better than existing uncertain QD methods. This suggests that considering the performance-reproducibility trade-off unlocks important stepping stones that are usually missed when only performance is optimised.

Quality-Diversity (QD) has demonstrated potential in discovering collections of diverse solutions to optimisation problems. Originally designed for deterministic environments, QD has been extended to noisy, stochastic, or uncertain domains through various Uncertain-QD (UQD) methods. However, the large number of UQD methods, each with unique constraints, makes selecting the most suitable one challenging. To remedy this situation, we present two contributions: first, the Extract-QD Framework (EQD Framework), and second, Extract-MAP-Elites (EME), a new method derived from it. The EQD Framework unifies existing approaches within a modular view, and facilitates developing novel methods by interchanging modules. We use it to derive EME, a novel method that consistently outperforms or matches the best existing methods on standard benchmarks, while previous methods show varying performance. In a second experiment, we show how our EQD Framework can be used to augment existing QD algorithms and, in particular, the well-established Policy-Gradient-Assisted-ME method, and demonstrate improved performance in uncertain domains at no additional evaluation cost. For any new uncertain task, our contributions now provide EME as a reliable "first guess" method, and the EQD Framework as a tool for developing task-specific approaches. Together, these contributions aim to lower the cost of adopting UQD insights in QD applications.

A hallmark of intelligence is the ability to exhibit a wide range of effective behaviors. Inspired by this principle, Quality-Diversity algorithms, such as MAP-Elites, are evolutionary methods designed to generate a set of diverse and high-fitness solutions. However, as a genetic algorithm, MAP-Elites relies on random mutations, which can become inefficient in high-dimensional search spaces, thus limiting its scalability to more complex domains, such as learning to control agents directly from high-dimensional inputs. To address this limitation, advanced methods like PGA-MAP-Elites and DCG-MAP-Elites have been developed, which combine actor-critic techniques from Reinforcement Learning with MAP-Elites, significantly enhancing the performance and efficiency of Quality-Diversity algorithms in complex, high-dimensional tasks. While these methods have successfully leveraged the trained critic to guide more effective mutations, the potential of the trained actor remains underutilized in improving both the quality and diversity of the evolved population. In this work, we introduce DCRL-MAP-Elites, an extension of DCG-MAP-Elites that utilizes the descriptor-conditioned actor as a generative model to produce diverse solutions, which are then injected into the offspring batch at each generation. Additionally, we present an empirical analysis of the fitness and descriptor reproducibility of the solutions discovered by each algorithm. Finally, we present a second empirical analysis shedding light on the synergies between the different variations operators and explaining the performance improvement from PGA-MAP-Elites to DCRL-MAP-Elites.

Many applications in Reinforcement Learning (RL) usually have noise or stochasticity present in the environment. Beyond their impact on learning, these uncertainties lead the exact same policy to perform differently, i.e. yield different return, from one roll-out to another. Common evaluation procedures in RL summarise the consequent return distributions using solely the expected return, which does not account for the spread of the distribution. Our work defines this spread as the policy reproducibility: the ability of a policy to obtain similar performance when rolled out many times, a crucial property in some real-world applications. We highlight that existing procedures that only use the expected return are limited on two fronts: first an infinite number of return distributions with a wide range of performance-reproducibility trade-offs can have the same expected return, limiting its effectiveness when used for comparing policies; second, the expected return metric does not leave any room for practitioners to choose the best trade-off value for considered applications. In this work, we address these limitations by recommending the use of Lower Confidence Bound, a metric taken from Bayesian optimisation that provides the user with a preference parameter to choose a desired performance-reproducibility trade-off. We also formalise and quantify policy reproducibility, and demonstrate the benefit of our metrics using extensive experiments of popular RL algorithms on common uncertain RL tasks.

With the development of fast and massively parallel evaluations in many domains, Quality-Diversity (QD) algorithms, that already proved promising in a large range of applications, have seen their potential multiplied. However, we have yet to understand how to best use a large number of evaluations as using them for random variations alone is not always effective. High-dimensional search spaces are a typical situation where random variations struggle to effectively search. Another situation is uncertain settings where solutions can appear better than they truly are and naively evaluating more solutions might mislead QD algorithms. In this work, we propose MAP-Elites-Multi-ES (MEMES), a novel QD algorithm based on Evolution Strategies (ES) designed to exploit fast parallel evaluations more effectively. MEMES maintains multiple (up to ~ 100) simultaneous ES processes, each with its own independent objective and reset mechanism designed for QD optimisation, all on just a single GPU. We show that MEMES outperforms both gradient-based and mutation-based QD algorithms on black-box optimisation and QD-Reinforcement-Learning tasks, demonstrating its benefit across domains. Additionally, our approach outperforms sampling-based QD methods in uncertain domains when given the same evaluation budget. Overall, MEMES generates reproducible solutions that are high-performing and diverse through large-scale ES optimisation on easily accessible hardware.

QDax is an open-source library with a streamlined and modular API for Quality-Diversity (QD) optimisation algorithms in Jax. The library serves as a versatile tool for optimisation purposes, ranging from black-box optimisation to continuous control. QDax offers implementations of popular QD, Neuroevolution, and Reinforcement Learning (RL) algorithms, supported by various examples. All the implementations can be just-in-time compiled with Jax, facilitating efficient execution across multiple accelerators, including GPUs and TPUs. These implementations effectively demonstrate the framework's flexibility and user-friendliness, easing experimentation for research purposes. Furthermore, the library is thoroughly documented and has 93% test coverage.

Quality-Diversity optimisation (QD) has proven to yield promising results across a broad set of applications. However, QD approaches struggle in the presence of uncertainty in the environment, as it impacts their ability to quantify the true performance and novelty of solutions. This problem has been highlighted multiple times independently in previous literature. In this work, we propose to uniformise the view on this problem through four main contributions. First, we formalise a common framework for uncertain domains: the Uncertain QD setting, a special case of QD in which fitness and descriptors for each solution are no longer fixed values but distribution over possible values. Second, we propose a new methodology to evaluate Uncertain QD approaches, relying on a new per-generation sampling budget and a set of existing and new metrics specifically designed for Uncertain QD. Third, we propose three new Uncertain QD algorithms: Archive-sampling, Parallel-Adaptivesampling and Deep-Grid-sampling. We propose these approaches taking into account recent advances in the QD community toward the use of hardware acceleration that enable large numbers of parallel evaluations and make sampling an affordable approach to uncertainty. Our final and fourth contribution is to use this new framework and the associated comparison methods to benchmark existing and novel approaches. We demonstrate once again the limitation of MAP-Elites in uncertain domains and highlight the performance of the existing Deep-Grid approach, and of our new algorithms. The goal of this framework and methods is to become an instrumental benchmark for future works considering Uncertain QD.

Quality-Diversity algorithms, such as MAP-Elites, are a branch of Evolutionary Computation generating collections of diverse and high-performing solutions, that have been successfully applied to a variety of domains and particularly in evolutionary robotics. However, MAP-Elites performs a divergent search based on random mutations originating from Genetic Algorithms, and thus, is limited to evolving populations of low-dimensional solutions. PGA-MAP-Elites overcomes this limitation by integrating a gradient-based variation operator inspired by Deep Reinforcement Learning which enables the evolution of large neural networks. Although high-performingin many environments, PGA-MAP-Elites fails on several tasks where the convergent search of the gradient-based operator does not direct mutations towards archive-improving solutions. In this work, we present two contributions: (1) we enhance the Policy Gradient variation operator with a descriptor-conditioned critic that improves the archive across the entire descriptor space, (2) we exploit the actor-critic training to learn a descriptor-conditioned policy at no additional cost, distilling the knowledge of the archive into one single versatile policy that can execute the entire range of behaviors contained in the archive. Our algorithm, DCG-MAP-Elites improves the QD score over PGA-MAP-Elites by 82% on average, on a set of challenging locomotion tasks.

Quality-Diversity (QD) algorithms are designed to generate collections of high-performing solutions while maximizing their diversity in a given descriptor space. However, in the presence of unpredictable noise, the fitness and descriptor of the same solution can differ significantly from one evaluation to another, leading to uncertainty in the estimation of such values. Given the elitist nature of QD algorithms, they commonly end up with many degenerate solutions in such noisy settings. In this work, we introduce Archive Reproducibility Improvement Algorithm (ARIA); a plug-and-play approach that improves the reproducibility of the solutions present in an archive. We propose it as a separate optimization module, relying on natural evolution strategies, that can be executed on top of any QD algorithm. Our module mutates solutions to (1) optimize their probability of belonging to their niche, and (2) maximize their fitness. The performance of our method is evaluated on various tasks, including a classical optimization problem and two high-dimensional control tasks in simulated robotic environments. We show that our algorithm enhances the quality and descriptor space coverage of any given archive by at least 50%.

The synergies between Quality-Diversity (QD) and Deep Reinforcement Learning (RL) have led to powerful hybrid QD-RL algorithms that have shown tremendous potential, and bring the best of both fields. However, only a single deep RL algorithm (TD3) has been used in prior hybrid methods despite notable progress made by other RL algorithms. Additionally, there are fundamental differences in the optimization procedures between QD and RL which would benefit from a more principled approach. We propose Generalized Actor-Critic QD-RL, a unified modular framework for actor-critic deep RL methods in the QD-RL setting. This framework provides a path to study insights from Deep RL in the QD-RL setting, which is an important and efficient way to make progress in QD-RL. We introduce two new algorithms, PGA-ME (SAC) and PGA-ME (DroQ) which apply recent advancements in Deep RL to the QD-RL setting, and solve the humanoid environment which was not possible using existing QD-RL algorithms. However, we also find that not all insights from Deep RL can be effectively translated to QD-RL. Critically, this work also demonstrates that the actor-critic models in QD-RL are generally insuficiently trained and performance gains can be achieved without any additional environment evaluations.

Quality-Diversity algorithms, among which are the Multi-dimensional Archive of Phenotypic Elites (MAP-Elites), have emerged as powerful alternatives to performance-only optimisation approaches as they enable generating collections of diverse and high-performing solutions to an optimisation problem. However, they are often limited to low-dimensional search spaces and deterministic environments. The recently introduced Policy Gradient Assisted MAP-Elites (PGA-MAP-Elites) algorithm overcomes this limitation by pairing the traditional Genetic operator of MAP-Elites with a gradient-based operator inspired by deep reinforcement learning. This new operator guides mutations toward high-performing solutions using policy gradients (PG). In this work, we propose an in-depth study of PGA-MAP-Elites. We demonstrate the benefits of PG on the performance of the algorithm and the reproducibility of the generated solutions when considering uncertain domains. We firstly prove that PGA-MAP-Elites is highly performant in both deterministic and uncertain high-dimensional environments, decorrelating the two challenges it tackles. Secondly, we show that in addition to outperforming all the considered baselines, the collections of solutions generated by PGA-MAP-Elites are highly reproducible in uncertain environments, approaching the reproducibility of solutions found by Quality-Diversity approaches built specifically for uncertain applications. Finally, we propose an ablation and in-depth analysis of the dynamic of the PG-based variation. We demonstrate that the PG variation operator is determinant to guarantee the performance of PGA-MAP-Elites but is only essential during the early stage of the process, where it finds high-performing regions of the search space.