Reinforcement learning (RL) systems have countless applications, from energy-grid management to protein design. However, such real-world scenarios are often extremely difficult, combinatorial in nature, and require complex coordination between multiple agents. This level of complexity can cause even state-of-the-art RL systems, trained until convergence, to hit a performance ceiling which they are unable to break out of with zero-shot inference. Meanwhile, many digital or simulation-based applications allow for an inference phase that utilises a specific time and compute budget to explore multiple attempts before outputting a final solution. In this work, we show that such an inference phase employed at execution time, and the choice of a corresponding inference strategy, are key to breaking the performance ceiling observed in complex multi-agent RL problems. Our main result is striking: we can obtain up to a 126% and, on average, a 45% improvement over the previous state-of-the-art across 17 tasks, using only a couple seconds of extra wall-clock time during execution. We also demonstrate promising compute scaling properties, supported by over 60k experiments, making it the largest study on inference strategies for complex RL to date. We make all of our experimental data and code available.

Routing Problems are central to many real-world applications, yet remain challenging due to their (NP-)hard nature. Amongst existing approaches, heuristics often offer the best trade-off between quality and scalability, making them suitable for industrial use. While Reinforcement Learning (RL) offers a flexible framework for designing heuristics, its adoption over handcrafted heuristics remains incomplete. Existing learned methods still lack the ability to adapt to specific instances and fully leverage the available computational budget. Current best methods either rely on a collection of pre-trained policies, or on RL fine-tuning; hence failing to fully utilize newly available information within the constraints of the budget. In response, we present MEMENTO, an approach that leverages memory to improve the search of neural solvers at inference. MEMENTO updates the action distribution dynamically based on the outcome of previous decisions. We validate its effectiveness on Traveling Salesman and Capacitated Vehicle Routing problems, demonstrating its superiority over tree-search and policy-gradient fine-tuning; and showing that it can be zero-shot combined with diversity-based solvers. We successfully train all RL auto-regressive solvers on large instances, and verify MEMENTO's scalability and data-efficiency: pushing the state-of-the-art on 11 out of 12 evaluated tasks.

A key challenge in offline multi-agent reinforcement learning (MARL) is achieving effective many-agent multi-step coordination in complex environments. In this work, we propose Oryx, a novel algorithm for offline cooperative MARL to directly address this challenge. Oryx adapts the recently proposed retention-based architecture Sable and combines it with a sequential form of implicit constraint Q-learning (ICQ), to develop a novel offline autoregressive policy update scheme. This allows Oryx to solve complex coordination challenges while maintaining temporal coherence over long trajectories. We evaluate Oryx across a diverse set of benchmarks from prior works—SMAC, RWARE, and Multi-Agent MuJoCo—covering tasks of both discrete and continuous control, varying in scale and difficulty. Oryx achieves state-of-the-art performance on more than 80% of the 65 tested datasets, outperforming prior offline MARL methods and demonstrating robust generalisation across domains with many agents and long horizons. Finally, we introduce new datasets to push the limits of many-agent coordination in offline MARL, and demonstrate Oryx's superior ability to scale effectively in such settings.

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.

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 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.

In the context of neuroevolution, Quality-Diversity algorithms have proven effective in generating repertoires of diverse and efficient policies by relying on the definition of a behavior space. A natural goal induced by the creation of such a repertoire is trying to achieve behaviors on demand, which can be done by running the corresponding policy from the repertoire. However, in uncertain environments, two problems arise. First, policies can lack robustness and repeatability, meaning that multiple episodes under slightly different conditions often result in very different behaviors. Second, due to the discrete nature of the repertoire, solutions vary discontinuously. Here we present a new approach to achieve behavior-conditioned trajectory generation based on two mechanisms: First, MAP-Elites Low-Spread (ME-LS), which constrains the selection of solutions to those that are the most consistent in the behavior space. Second, the Quality-Diversity Transformer (QDT), a Transformer-based model conditioned on continuous behavior descriptors, which trains on a dataset generated by policies from a ME-LS repertoire and learns to autoregressively generate sequences of actions that achieve target behaviors. Results show that ME-LS produces consistent and robust policies, and that its combination with the QDT yields a single policy capable of achieving diverse behaviors on demand with high accuracy.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions, but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy, or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches in 9 out of 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.

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.

A fascinating aspect of nature lies in its ability to produce a large and diverse collection of organisms that are all high-performing in their niche. By contrast, most AI algorithms focus on finding a single eficient solution to a given problem. Aiming for diversity in addition to performance is a convenient way to deal with the exploration-exploitation trade-off that plays a central role in learning. It also allows for increased robustness when the returned collection contains several working solutions to the considered problem, making it well-suited for real applications such as robotics. Quality-Diversity (QD) methods are evolutionary algorithms designed for this purpose. This paper proposes a novel algorithm, qd-pg, which combines the strength of Policy Gradient algorithms and Quality Diversity approaches to produce a collection of diverse and high-performing neural policies in continuous control environments. The main contribution of this work is the introduction of a Diversity Policy Gradient (DPG) that exploits information at the time-step level to drive policies towards more diversity in a sample-efficient manner. Specifically, qd-pg selects neural controllers from a map-elites grid and uses two gradient-based mutation operators to improve both quality and diversity. Our results demonstrate that qd-pg is significantly more sample-eficient than its evolutionary competitors.