Chris Lu

Sandhini Agarwal, Lama Ahmad, Jason Ai et al. · openai

We present gpt-oss-120b and gpt-oss-20b, two open-weight reasoning models that push the frontier of accuracy and inference cost. The models use an efficient mixture-of-expert transformer architecture and are trained using large-scale distillation and reinforcement learning. We optimize the models to have strong agentic capabilities (deep research browsing, python tool use, and support for developer-provided functions), all while using a rendered chat format that enables clear instruction following and role delineation. Both models achieve strong results on benchmarks ranging from mathematics, coding, and safety. We release the model weights, inference implementations, tool environments, and tokenizers under an Apache 2.0 license to enable broad use and further research.

Alexander Rutherford, Benjamin Ellis, Matteo Gallici et al. · deepmind, meta-ai

Benchmarks are crucial in the development of machine learning algorithms, with available environments significantly influencing reinforcement learning (RL) research. Traditionally, RL environments run on the CPU, which limits their scalability with typical academic compute. However, recent advancements in JAX have enabled the wider use of hardware acceleration, enabling massively parallel RL training pipelines and environments. While this has been successfully applied to single-agent RL, it has not yet been widely adopted for multi-agent scenarios. In this paper, we present JaxMARL, the first open-source, Python-based library that combines GPU-enabled efficiency with support for a large number of commonly used MARL environments and popular baseline algorithms. Our experiments show that, in terms of wall clock time, our JAX-based training pipeline is around 14 times faster than existing approaches, and up to 12500x when multiple training runs are vectorized. This enables efficient and thorough evaluations, potentially alleviating the evaluation crisis in the field. We also introduce and benchmark SMAX, a JAX-based approximate reimplementation of the popular StarCraft Multi-Agent Challenge, which removes the need to run the StarCraft II game engine. This not only enables GPU acceleration, but also provides a more flexible MARL environment, unlocking the potential for self-play, meta-learning, and other future applications in MARL. The code is available at https://github.com/flairox/jaxmarl.

Chris Lu, Cong Lu, Robert Tjarko Lange et al. · deepmind

One of the grand challenges of artificial general intelligence is developing agents capable of conducting scientific research and discovering new knowledge. While frontier models have already been used as aides to human scientists, e.g. for brainstorming ideas, writing code, or prediction tasks, they still conduct only a small part of the scientific process. This paper presents the first comprehensive framework for fully automatic scientific discovery, enabling frontier large language models to perform research independently and communicate their findings. We introduce The AI Scientist, which generates novel research ideas, writes code, executes experiments, visualizes results, describes its findings by writing a full scientific paper, and then runs a simulated review process for evaluation. In principle, this process can be repeated to iteratively develop ideas in an open-ended fashion, acting like the human scientific community. We demonstrate its versatility by applying it to three distinct subfields of machine learning: diffusion modeling, transformer-based language modeling, and learning dynamics. Each idea is implemented and developed into a full paper at a cost of less than $15 per paper. To evaluate the generated papers, we design and validate an automated reviewer, which we show achieves near-human performance in evaluating paper scores. The AI Scientist can produce papers that exceed the acceptance threshold at a top machine learning conference as judged by our automated reviewer. This approach signifies the beginning of a new era in scientific discovery in machine learning: bringing the transformative benefits of AI agents to the entire research process of AI itself, and taking us closer to a world where endless affordable creativity and innovation can be unleashed on the world's most challenging problems. Our code is open-sourced at https://github.com/SakanaAI/AI-Scientist

Aaditya Singh, Adam Fry, Adam Perelman et al. · berkeley, mila

This is the system card published alongside the OpenAI GPT-5 launch, August 2025. GPT-5 is a unified system with a smart and fast model that answers most questions, a deeper reasoning model for harder problems, and a real-time router that quickly decides which model to use based on conversation type, complexity, tool needs, and explicit intent (for example, if you say 'think hard about this' in the prompt). The router is continuously trained on real signals, including when users switch models, preference rates for responses, and measured correctness, improving over time. Once usage limits are reached, a mini version of each model handles remaining queries. This system card focuses primarily on gpt-5-thinking and gpt-5-main, while evaluations for other models are available in the appendix. The GPT-5 system not only outperforms previous models on benchmarks and answers questions more quickly, but -- more importantly -- is more useful for real-world queries. We've made significant advances in reducing hallucinations, improving instruction following, and minimizing sycophancy, and have leveled up GPT-5's performance in three of ChatGPT's most common uses: writing, coding, and health. All of the GPT-5 models additionally feature safe-completions, our latest approach to safety training to prevent disallowed content. Similarly to ChatGPT agent, we have decided to treat gpt-5-thinking as High capability in the Biological and Chemical domain under our Preparedness Framework, activating the associated safeguards. While we do not have definitive evidence that this model could meaningfully help a novice to create severe biological harm -- our defined threshold for High capability -- we have chosen to take a precautionary approach.

Chris Lu, Yannick Schroecker, Albert Gu et al.

Structured state space sequence (S4) models have recently achieved state-of-the-art performance on long-range sequence modeling tasks. These models also have fast inference speeds and parallelisable training, making them potentially useful in many reinforcement learning settings. We propose a modification to a variant of S4 that enables us to initialise and reset the hidden state in parallel, allowing us to tackle reinforcement learning tasks. We show that our modified architecture runs asymptotically faster than Transformers in sequence length and performs better than RNN's on a simple memory-based task. We evaluate our modified architecture on a set of partially-observable environments and find that, in practice, our model outperforms RNN's while also running over five times faster. Then, by leveraging the model's ability to handle long-range sequences, we achieve strong performance on a challenging meta-learning task in which the agent is given a randomly-sampled continuous control environment, combined with a randomly-sampled linear projection of the environment's observations and actions. Furthermore, we show the resulting model can adapt to out-of-distribution held-out tasks. Overall, the results presented in this paper show that structured state space models are fast and performant for in-context reinforcement learning tasks. We provide code at https://github.com/luchris429/popjaxrl.

Chris Lu, Jakub Grudzien Kuba, Alistair Letcher et al. · deepmind

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

Matthew Thomas Jackson, Minqi Jiang, Jack Parker-Holder et al. · oxford

The past decade has seen vast progress in deep reinforcement learning (RL) on the back of algorithms manually designed by human researchers. Recently, it has been shown that it is possible to meta-learn update rules, with the hope of discovering algorithms that can perform well on a wide range of RL tasks. Despite impressive initial results from algorithms such as Learned Policy Gradient (LPG), there remains a generalization gap when these algorithms are applied to unseen environments. In this work, we examine how characteristics of the meta-training distribution impact the generalization performance of these algorithms. Motivated by this analysis and building on ideas from Unsupervised Environment Design (UED), we propose a novel approach for automatically generating curricula to maximize the regret of a meta-learned optimizer, in addition to a novel approximation of regret, which we name algorithmic regret (AR). The result is our method, General RL Optimizers Obtained Via Environment Design (GROOVE). In a series of experiments, we show that GROOVE achieves superior generalization to LPG, and evaluate AR against baseline metrics from UED, identifying it as a critical component of environment design in this setting. We believe this approach is a step towards the discovery of truly general RL algorithms, capable of solving a wide range of real-world environments.

Robert Tjarko Lange, Tom Schaul, Yutian Chen et al.

Optimizing functions without access to gradients is the remit of black-box methods such as evolution strategies. While highly general, their learning dynamics are often times heuristic and inflexible - exactly the limitations that meta-learning can address. Hence, we propose to discover effective update rules for evolution strategies via meta-learning. Concretely, our approach employs a search strategy parametrized by a self-attention-based architecture, which guarantees the update rule is invariant to the ordering of the candidate solutions. We show that meta-evolving this system on a small set of representative low-dimensional analytic optimization problems is sufficient to discover new evolution strategies capable of generalizing to unseen optimization problems, population sizes and optimization horizons. Furthermore, the same learned evolution strategy can outperform established neuroevolution baselines on supervised and continuous control tasks. As additional contributions, we ablate the individual neural network components of our method; reverse engineer the learned strategy into an explicit heuristic form, which remains highly competitive; and show that it is possible to self-referentially train an evolution strategy from scratch, with the learned update rule used to drive the outer meta-learning loop.

Alexander David Goldie, Chris Lu, Matthew Thomas Jackson et al.

While reinforcement learning (RL) holds great potential for decision making in the real world, it suffers from a number of unique difficulties which often need specific consideration. In particular: it is highly non-stationary; suffers from high degrees of plasticity loss; and requires exploration to prevent premature convergence to local optima and maximize return. In this paper, we consider whether learned optimization can help overcome these problems. Our method, Learned Optimization for Plasticity, Exploration and Non-stationarity (OPEN), meta-learns an update rule whose input features and output structure are informed by previously proposed solutions to these difficulties. We show that our parameterization is flexible enough to enable meta-learning in diverse learning contexts, including the ability to use stochasticity for exploration. Our experiments demonstrate that when meta-trained on single and small sets of environments, OPEN outperforms or equals traditionally used optimizers. Furthermore, OPEN shows strong generalization characteristics across a range of environments and agent architectures.

Stephen Zhao, Chris Lu, Roger Baker Grosse et al.

Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn such behaviour on more complex policy spaces parameterized by neural networks, partly because the update rule is sensitive to the policy parameterization. This problem is especially pronounced in the opponent modeling setting, where the opponent's policy is unknown and must be inferred from observations; in such settings, LOLA is ill-specified because behaviorally equivalent opponent policies can result in non-equivalent updates. To address this shortcoming, we reinterpret LOLA as approximating a proximal operator, and then derive a new algorithm, proximal LOLA (POLA), which uses the proximal formulation directly. Unlike LOLA, the POLA updates are parameterization invariant, in the sense that when the proximal objective has a unique optimum, behaviorally equivalent policies result in behaviorally equivalent updates. We then present practical approximations to the ideal POLA update, which we evaluate in several partially competitive environments with function approximation and opponent modeling. This empirically demonstrates that POLA achieves reciprocity-based cooperation more reliably than LOLA.

Robert Tjarko Lange, Tom Schaul, Yutian Chen et al.

Genetic algorithms constitute a family of black-box optimization algorithms, which take inspiration from the principles of biological evolution. While they provide a general-purpose tool for optimization, their particular instantiations can be heuristic and motivated by loose biological intuition. In this work we explore a fundamentally different approach: Given a sufficiently flexible parametrization of the genetic operators, we discover entirely new genetic algorithms in a data-driven fashion. More specifically, we parametrize selection and mutation rate adaptation as cross- and self-attention modules and use Meta-Black-Box-Optimization to evolve their parameters on a set of diverse optimization tasks. The resulting Learned Genetic Algorithm outperforms state-of-the-art adaptive baseline genetic algorithms and generalizes far beyond its meta-training settings. The learned algorithm can be applied to previously unseen optimization problems, search dimensions & evaluation budgets. We conduct extensive analysis of the discovered operators and provide ablation experiments, which highlight the benefits of flexible module parametrization and the ability to transfer (`plug-in') the learned operators to conventional genetic algorithms.

Andrew Jesson, Chris Lu, Gunshi Gupta et al.

This paper proposes a step toward approximate Bayesian inference in on-policy actor-critic deep reinforcement learning. It is implemented through three changes to the Asynchronous Advantage Actor-Critic (A3C) algorithm: (1) applying a ReLU function to advantage estimates, (2) spectral normalization of actor-critic weights, and (3) incorporating \emph{dropout as a Bayesian approximation}. We prove under standard assumptions that restricting policy updates to positive advantages optimizes for value by maximizing a lower bound on the value function plus an additive term. We show that the additive term is bounded proportional to the Lipschitz constant of the value function, which offers theoretical grounding for spectral normalization of critic weights. Finally, our application of dropout corresponds to approximate Bayesian inference over both the actor and critic parameters, which enables \textit{adaptive state-aware} exploration around the modes of the actor via Thompson sampling. We demonstrate significant improvements for median and interquartile mean metrics over A3C, PPO, SAC, and TD3 on the MuJoCo continuous control benchmark and improvement over PPO in the challenging ProcGen generalization benchmark.

Chris Lu, Timon Willi, Christian Schroeder de Witt et al.

In general-sum games, the interaction of self-interested learning agents commonly leads to collectively worst-case outcomes, such as defect-defect in the iterated prisoner's dilemma (IPD). To overcome this, some methods, such as Learning with Opponent-Learning Awareness (LOLA), shape their opponents' learning process. However, these methods are myopic since only a small number of steps can be anticipated, are asymmetric since they treat other agents as naive learners, and require the use of higher-order derivatives, which are calculated through white-box access to an opponent's differentiable learning algorithm. To address these issues, we propose Model-Free Opponent Shaping (M-FOS). M-FOS learns in a meta-game in which each meta-step is an episode of the underlying inner game. The meta-state consists of the inner policies, and the meta-policy produces a new inner policy to be used in the next episode. M-FOS then uses generic model-free optimisation methods to learn meta-policies that accomplish long-horizon opponent shaping. Empirically, M-FOS near-optimally exploits naive learners and other, more sophisticated algorithms from the literature. For example, to the best of our knowledge, it is the first method to learn the well-known Zero-Determinant (ZD) extortion strategy in the IPD. In the same settings, M-FOS leads to socially optimal outcomes under meta-self-play. Finally, we show that M-FOS can be scaled to high-dimensional settings.

Chris Lu, Michael Beukman, Michael Matthews et al.

Human intelligence emerged through the process of natural selection and evolution on Earth. We investigate what it would take to re-create this process in silico. While past work has often focused on low-level processes (such as simulating physics or chemistry), we instead take a more targeted approach, aiming to evolve agents that can accumulate open-ended culture and technologies across generations. Towards this, we present JaxLife: an artificial life simulator in which embodied agents, parameterized by deep neural networks, must learn to survive in an expressive world containing programmable systems. First, we describe the environment and show that it can facilitate meaningful Turing-complete computation. We then analyze the evolved emergent agents' behavior, such as rudimentary communication protocols, agriculture, and tool use. Finally, we investigate how complexity scales with the amount of compute used. We believe JaxLife takes a step towards studying evolved behavior in more open-ended simulations. Our code is available at https://github.com/luchris429/JaxLife

Sascha Frey, Kang Li, Peer Nagy et al.

Financial exchanges across the world use limit order books (LOBs) to process orders and match trades. For research purposes it is important to have large scale efficient simulators of LOB dynamics. LOB simulators have previously been implemented in the context of agent-based models (ABMs), reinforcement learning (RL) environments, and generative models, processing order flows from historical data sets and hand-crafted agents alike. For many applications, there is a requirement for processing multiple books, either for the calibration of ABMs or for the training of RL agents. We showcase the first GPU-enabled LOB simulator designed to process thousands of books in parallel, with a notably reduced per-message processing time. The implementation of our simulator - JAX-LOB - is based on design choices that aim to best exploit the powers of JAX without compromising on the realism of LOB-related mechanisms. We integrate JAX-LOB with other JAX packages, to provide an example of how one may address an optimal execution problem with reinforcement learning, and to share some preliminary results from end-to-end RL training on GPUs.

Chris Lu, Timon Willi, Alistair Letcher et al.

Adversarial attacks in reinforcement learning (RL) often assume highly-privileged access to the victim's parameters, environment, or data. Instead, this paper proposes a novel adversarial setting called a Cheap Talk MDP in which an Adversary can merely append deterministic messages to the Victim's observation, resulting in a minimal range of influence. The Adversary cannot occlude ground truth, influence underlying environment dynamics or reward signals, introduce non-stationarity, add stochasticity, see the Victim's actions, or access their parameters. Additionally, we present a simple meta-learning algorithm called Adversarial Cheap Talk (ACT) to train Adversaries in this setting. We demonstrate that an Adversary trained with ACT still significantly influences the Victim's training and testing performance, despite the highly constrained setting. Affecting train-time performance reveals a new attack vector and provides insight into the success and failure modes of existing RL algorithms. More specifically, we show that an ACT Adversary is capable of harming performance by interfering with the learner's function approximation, or instead helping the Victim's performance by outputting useful features. Finally, we show that an ACT Adversary can manipulate messages during train-time to directly and arbitrarily control the Victim at test-time. Project video and code are available at https://sites.google.com/view/adversarial-cheap-talk

Chris Lu, Sebastian Towers, Jakob Foerster

Meta-learning, the notion of learning to learn, enables learning systems to quickly and flexibly solve new tasks. This usually involves defining a set of outer-loop meta-parameters that are then used to update a set of inner-loop parameters. Most meta-learning approaches use complicated and computationally expensive bi-level optimisation schemes to update these meta-parameters. Ideally, systems should perform multiple orders of meta-learning, i.e. to learn to learn to learn and so on, to accelerate their own learning. Unfortunately, standard meta-learning techniques are often inappropriate for these higher-order meta-parameters because the meta-optimisation procedure becomes too complicated or unstable. Inspired by the higher-order meta-learning we observe in real-world evolution, we show that using simple population-based evolution implicitly optimises for arbitrarily-high order meta-parameters. First, we theoretically prove and empirically show that population-based evolution implicitly optimises meta-parameters of arbitrarily-high order in a simple setting. We then introduce a minimal self-referential parameterisation, which in principle enables arbitrary-order meta-learning. Finally, we show that higher-order meta-learning improves performance on time series forecasting tasks.

Yutaro Yamada, Robert Tjarko Lange, Cong Lu et al.

AI is increasingly playing a pivotal role in transforming how scientific discoveries are made. We introduce The AI Scientist-v2, an end-to-end agentic system capable of producing the first entirely AI generated peer-review-accepted workshop paper. This system iteratively formulates scientific hypotheses, designs and executes experiments, analyzes and visualizes data, and autonomously authors scientific manuscripts. Compared to its predecessor (v1, Lu et al., 2024 arXiv:2408.06292), The AI Scientist-v2 eliminates the reliance on human-authored code templates, generalizes effectively across diverse machine learning domains, and leverages a novel progressive agentic tree-search methodology managed by a dedicated experiment manager agent. Additionally, we enhance the AI reviewer component by integrating a Vision-Language Model (VLM) feedback loop for iterative refinement of content and aesthetics of the figures. We evaluated The AI Scientist-v2 by submitting three fully autonomous manuscripts to a peer-reviewed ICLR workshop. Notably, one manuscript achieved high enough scores to exceed the average human acceptance threshold, marking the first instance of a fully AI-generated paper successfully navigating a peer review. This accomplishment highlights the growing capability of AI in conducting all aspects of scientific research. We anticipate that further advancements in autonomous scientific discovery technologies will profoundly impact human knowledge generation, enabling unprecedented scalability in research productivity and significantly accelerating scientific breakthroughs, greatly benefiting society at large. We have open-sourced the code at https://github.com/SakanaAI/AI-Scientist-v2 to foster the future development of this transformative technology. We also discuss the role of AI in science, including AI safety.

Eduardo Pignatelli, Jarek Liesen, Robert Tjarko Lange et al.

As Deep Reinforcement Learning (Deep RL) research moves towards solving large-scale worlds, efficient environment simulations become crucial for rapid experimentation. However, most existing environments struggle to scale to high throughput, setting back meaningful progress. Interactions are typically computed on the CPU, limiting training speed and throughput, due to slower computation and communication overhead when distributing the task across multiple machines. Ultimately, Deep RL training is CPU-bound, and developing batched, fast, and scalable environments has become a frontier for progress. Among the most used Reinforcement Learning (RL) environments, MiniGrid is at the foundation of several studies on exploration, curriculum learning, representation learning, diversity, meta-learning, credit assignment, and language-conditioned RL, and still suffers from the limitations described above. In this work, we introduce NAVIX, a re-implementation of MiniGrid in JAX. NAVIX achieves over 200 000x speed improvements in batch mode, supporting up to 2048 agents in parallel on a single Nvidia A100 80 GB. This reduces experiment times from one week to 15 minutes, promoting faster design iterations and more scalable RL model development.

Matthew Thomas Jackson, Chris Lu, Louis Kirsch et al.

Recent advancements in meta-learning have enabled the automatic discovery of novel reinforcement learning algorithms parameterized by surrogate objective functions. To improve upon manually designed algorithms, the parameterization of this learned objective function must be expressive enough to represent novel principles of learning (instead of merely recovering already established ones) while still generalizing to a wide range of settings outside of its meta-training distribution. However, existing methods focus on discovering objective functions that, like many widely used objective functions in reinforcement learning, do not take into account the total number of steps allowed for training, or "training horizon". In contrast, humans use a plethora of different learning objectives across the course of acquiring a new ability. For instance, students may alter their studying techniques based on the proximity to exam deadlines and their self-assessed capabilities. This paper contends that ignoring the optimization time horizon significantly restricts the expressive potential of discovered learning algorithms. We propose a simple augmentation to two existing objective discovery approaches that allows the discovered algorithm to dynamically update its objective function throughout the agent's training procedure, resulting in expressive schedules and increased generalization across different training horizons. In the process, we find that commonly used meta-gradient approaches fail to discover such adaptive objective functions while evolution strategies discover highly dynamic learning rules. We demonstrate the effectiveness of our approach on a wide range of tasks and analyze the resulting learned algorithms, which we find effectively balance exploration and exploitation by modifying the structure of their learning rules throughout the agent's lifetime.

Akarsh Kumar, Chris Lu, Louis Kirsch et al.

With the recent Nobel Prize awarded for radical advances in protein discovery, foundation models (FMs) for exploring large combinatorial spaces promise to revolutionize many scientific fields. Artificial Life (ALife) has not yet integrated FMs, thus presenting a major opportunity for the field to alleviate the historical burden of relying chiefly on manual design and trial-and-error to discover the configurations of lifelike simulations. This paper presents, for the first time, a successful realization of this opportunity using vision-language FMs. The proposed approach, called Automated Search for Artificial Life (ASAL), (1) finds simulations that produce target phenomena, (2) discovers simulations that generate temporally open-ended novelty, and (3) illuminates an entire space of interestingly diverse simulations. Because of the generality of FMs, ASAL works effectively across a diverse range of ALife substrates including Boids, Particle Life, Game of Life, Lenia, and Neural Cellular Automata. A major result highlighting the potential of this technique is the discovery of previously unseen Lenia and Boids lifeforms, as well as cellular automata that are open-ended like Conway's Game of Life. Additionally, the use of FMs allows for the quantification of previously qualitative phenomena in a human-aligned way. This new paradigm promises to accelerate ALife research beyond what is possible through human ingenuity alone.

Michael Matthews, Michael Beukman, Chris Lu et al.

While large models trained with self-supervised learning on offline datasets have shown remarkable capabilities in text and image domains, achieving the same generalisation for agents that act in sequential decision problems remains an open challenge. In this work, we take a step towards this goal by procedurally generating tens of millions of 2D physics-based tasks and using these to train a general reinforcement learning (RL) agent for physical control. To this end, we introduce Kinetix: an open-ended space of physics-based RL environments that can represent tasks ranging from robotic locomotion and grasping to video games and classic RL environments, all within a unified framework. Kinetix makes use of our novel hardware-accelerated physics engine Jax2D that allows us to cheaply simulate billions of environment steps during training. Our trained agent exhibits strong physical reasoning capabilities in 2D space, being able to zero-shot solve unseen human-designed environments. Furthermore, fine-tuning this general agent on tasks of interest shows significantly stronger performance than training an RL agent *tabula rasa*. This includes solving some environments that standard RL training completely fails at. We believe this demonstrates the feasibility of large scale, mixed-quality pre-training for online RL and we hope that Kinetix will serve as a useful framework to investigate this further.

Akbir Khan, Timon Willi, Newton Kwan et al.

In multi-agent settings with mixed incentives, methods developed for zero-sum games have been shown to lead to detrimental outcomes. To address this issue, opponent shaping (OS) methods explicitly learn to influence the learning dynamics of co-players and empirically lead to improved individual and collective outcomes. However, OS methods have only been evaluated in low-dimensional environments due to the challenges associated with estimating higher-order derivatives or scaling model-free meta-learning. Alternative methods that scale to more complex settings either converge to undesirable solutions or rely on unrealistic assumptions about the environment or co-players. In this paper, we successfully scale an OS-based approach to general-sum games with temporally-extended actions and long-time horizons for the first time. After analysing the representations of the meta-state and history used by previous algorithms, we propose a simplified version called Shaper. We show empirically that Shaper leads to improved individual and collective outcomes in a range of challenging settings from literature. We further formalize a technique previously implicit in the literature, and analyse its contribution to opponent shaping. We show empirically that this technique is helpful for the functioning of prior methods in certain environments. Lastly, we show that previous environments, such as the CoinGame, are inadequate for analysing temporally-extended general-sum interactions.

Steven Morad, Chris Lu, Ryan Kortvelesy et al.

Memory models such as Recurrent Neural Networks (RNNs) and Transformers address Partially Observable Markov Decision Processes (POMDPs) by mapping trajectories to latent Markov states. Neither model scales particularly well to long sequences, especially compared to an emerging class of memory models called Linear Recurrent Models. We discover that the recurrent update of these models resembles a monoid, leading us to reformulate existing models using a novel monoid-based framework that we call memoroids. We revisit the traditional approach to batching in recurrent reinforcement learning, highlighting theoretical and empirical deficiencies. We leverage memoroids to propose a batching method that improves sample efficiency, increases the return, and simplifies the implementation of recurrent loss functions in reinforcement learning.

Alexandra Souly, Timon Willi, Akbir Khan et al.

Reinforcement learning solutions have great success in the 2-player general sum setting. In this setting, the paradigm of Opponent Shaping (OS), in which agents account for the learning of their co-players, has led to agents which are able to avoid collectively bad outcomes, whilst also maximizing their reward. These methods have currently been limited to 2-player game. However, the real world involves interactions with many more agents, with interactions on both local and global scales. In this paper, we extend Opponent Shaping (OS) methods to environments involving multiple co-players and multiple shaping agents. We evaluate on over 4 different environments, varying the number of players from 3 to 5, and demonstrate that model-based OS methods converge to equilibrium with better global welfare than naive learning. However, we find that when playing with a large number of co-players, OS methods' relative performance reduces, suggesting that in the limit OS methods may not perform well. Finally, we explore scenarios where more than one OS method is present, noticing that within games requiring a majority of cooperating agents, OS methods converge to outcomes with poor global welfare.

Carlo Alfano, Sebastian Towers, Silvia Sapora et al.

Policy Mirror Descent (PMD) is a popular framework in reinforcement learning, serving as a unifying perspective that encompasses numerous algorithms. These algorithms are derived through the selection of a mirror map and enjoy finite-time convergence guarantees. Despite its popularity, the exploration of PMD's full potential is limited, with the majority of research focusing on a particular mirror map -- namely, the negative entropy -- which gives rise to the renowned Natural Policy Gradient (NPG) method. It remains uncertain from existing theoretical studies whether the choice of mirror map significantly influences PMD's efficacy. In our work, we conduct empirical investigations to show that the conventional mirror map choice (NPG) often yields less-than-optimal outcomes across several standard benchmark environments. Using evolutionary strategies, we identify more efficient mirror maps that enhance the performance of PMD. We first focus on a tabular environment, i.e. Grid-World, where we relate existing theoretical bounds with the performance of PMD for a few standard mirror maps and the learned one. We then show that it is possible to learn a mirror map that outperforms the negative entropy in more complex environments, such as the MinAtar suite. Our results suggest that mirror maps generalize well across various environments, raising questions about how to best match a mirror map to an environment's structure and characteristics.

Andrei Lupu, Chris Lu, Jarek Liesen et al.

Dataset distillation aims to condense large datasets into a small number of synthetic examples that can be used as drop-in replacements when training new models. It has applications to interpretability, neural architecture search, privacy, and continual learning. Despite strong successes in supervised domains, such methods have not yet been extended to reinforcement learning, where the lack of a fixed dataset renders most distillation methods unusable. Filling the gap, we formalize behaviour distillation, a setting that aims to discover and then condense the information required for training an expert policy into a synthetic dataset of state-action pairs, without access to expert data. We then introduce Hallucinating Datasets with Evolution Strategies (HaDES), a method for behaviour distillation that can discover datasets of just four state-action pairs which, under supervised learning, train agents to competitive performance levels in continuous control tasks. We show that these datasets generalize out of distribution to training policies with a wide range of architectures and hyperparameters. We also demonstrate application to a downstream task, namely training multi-task agents in a zero-shot fashion. Beyond behaviour distillation, HaDES provides significant improvements in neuroevolution for RL over previous approaches and achieves SoTA results on one standard supervised dataset distillation task. Finally, we show that visualizing the synthetic datasets can provide human-interpretable task insights.

Jarek Liesen, Chris Lu, Andrei Lupu et al.

Reinforcement learning (RL) agents are commonly trained and evaluated in the same environment. In contrast, humans often train in a specialized environment before being evaluated, such as studying a book before taking an exam. The potential of such specialized training environments is still vastly underexplored, despite their capacity to dramatically speed up training. The framework of synthetic environments takes a first step in this direction by meta-learning neural network-based Markov decision processes (MDPs). The initial approach was limited to toy problems and produced environments that did not transfer to unseen RL algorithms. We extend this approach in three ways: Firstly, we modify the meta-learning algorithm to discover environments invariant towards hyperparameter configurations and learning algorithms. Secondly, by leveraging hardware parallelism and introducing a curriculum on an agent's evaluation episode horizon, we can achieve competitive results on several challenging continuous control problems. Thirdly, we surprisingly find that contextual bandits enable training RL agents that transfer well to their evaluation environment, even if it is a complex MDP. Hence, we set up our experiments to train synthetic contextual bandits, which perform on par with synthetic MDPs, yield additional insights into the evaluation environment, and can speed up downstream applications.

Silvia Sapora, Gokul Swamy, Chris Lu et al.

Often times in imitation learning (IL), the environment we collect expert demonstrations in and the environment we want to deploy our learned policy in aren't exactly the same (e.g. demonstrations collected in simulation but deployment in the real world). Compared to policy-centric approaches to IL like behavioural cloning, reward-centric approaches like inverse reinforcement learning (IRL) often better replicate expert behaviour in new environments. This transfer is usually performed by optimising the recovered reward under the dynamics of the target environment. However, (a) we find that modern deep IL algorithms frequently recover rewards which induce policies far weaker than the expert, even in the same environment the demonstrations were collected in. Furthermore, (b) these rewards are often quite poorly shaped, necessitating extensive environment interaction to optimise effectively. We provide simple and scalable fixes to both of these concerns. For (a), we find that reward model ensembles combined with a slightly different training objective significantly improves re-training and transfer performance. For (b), we propose a novel evolution-strategies based method EvIL to optimise for a reward-shaping term that speeds up re-training in the target environment, closing a gap left open by the classical theory of IRL. On a suite of continuous control tasks, we are able to re-train policies in target (and source) environments more interaction-efficiently than prior work.

Chris Lu, Samuel Holt, Claudio Fanconi et al.

Offline preference optimization is a key method for enhancing and controlling the quality of Large Language Model (LLM) outputs. Typically, preference optimization is approached as an offline supervised learning task using manually-crafted convex loss functions. While these methods are based on theoretical insights, they are inherently constrained by human creativity, so the large search space of possible loss functions remains under explored. We address this by performing LLM-driven objective discovery to automatically discover new state-of-the-art preference optimization algorithms without (expert) human intervention. Specifically, we iteratively prompt an LLM to propose and implement new preference optimization loss functions based on previously-evaluated performance metrics. This process leads to the discovery of previously-unknown and performant preference optimization algorithms. The best performing of these we call Discovered Preference Optimization (DiscoPOP), a novel algorithm that adaptively blends logistic and exponential losses. Experiments demonstrate the state-of-the-art performance of DiscoPOP and its successful transfer to held-out tasks.

Jonathan Cook, Chris Lu, Edward Hughes et al.

Cultural accumulation drives the open-ended and diverse progress in capabilities spanning human history. It builds an expanding body of knowledge and skills by combining individual exploration with inter-generational information transmission. Despite its widespread success among humans, the capacity for artificial learning agents to accumulate culture remains under-explored. In particular, approaches to reinforcement learning typically strive for improvements over only a single lifetime. Generational algorithms that do exist fail to capture the open-ended, emergent nature of cultural accumulation, which allows individuals to trade-off innovation and imitation. Building on the previously demonstrated ability for reinforcement learning agents to perform social learning, we find that training setups which balance this with independent learning give rise to cultural accumulation. These accumulating agents outperform those trained for a single lifetime with the same cumulative experience. We explore this accumulation by constructing two models under two distinct notions of a generation: episodic generations, in which accumulation occurs via in-context learning and train-time generations, in which accumulation occurs via in-weights learning. In-context and in-weights cultural accumulation can be interpreted as analogous to knowledge and skill accumulation, respectively. To the best of our knowledge, this work is the first to present general models that achieve emergent cultural accumulation in reinforcement learning, opening up new avenues towards more open-ended learning systems, as well as presenting new opportunities for modelling human culture.

Kitty Fung, Qizhen Zhang, Chris Lu et al.

Learning in general-sum games often yields collectively sub-optimal results. Addressing this, opponent shaping (OS) methods actively guide the learning processes of other agents, empirically leading to improved individual and group performances in many settings. Early OS methods use higher-order derivatives to shape the learning of co-players, making them unsuitable for shaping multiple learning steps. Follow-up work, Model-free Opponent Shaping (M-FOS), addresses these by reframing the OS problem as a meta-game. In contrast to early OS methods, there is little theoretical understanding of the M-FOS framework. Providing theoretical guarantees for M-FOS is hard because A) there is little literature on theoretical sample complexity bounds for meta-reinforcement learning B) M-FOS operates in continuous state and action spaces, so theoretical analysis is challenging. In this work, we present R-FOS, a tabular version of M-FOS that is more suitable for theoretical analysis. R-FOS discretises the continuous meta-game MDP into a tabular MDP. Within this discretised MDP, we adapt the $R_{max}$ algorithm, most prominently used to derive PAC-bounds for MDPs, as the meta-learner in the R-FOS algorithm. We derive a sample complexity bound that is exponential in the cardinality of the inner state and action space and the number of agents. Our bound guarantees that, with high probability, the final policy learned by an R-FOS agent is close to the optimal policy, apart from a constant factor. Finally, we investigate how R-FOS's sample complexity scales in the size of state-action space. Our theoretical results on scaling are supported empirically in the Matching Pennies environment.

Qizhen Zhang, Chris Lu, Animesh Garg et al.

Reinforcement learning (RL) in partially observable, fully cooperative multi-agent settings (Dec-POMDPs) can in principle be used to address many real-world challenges such as controlling a swarm of rescue robots or a team of quadcopters. However, Dec-POMDPs are significantly harder to solve than single-agent problems, with the former being NEXP-complete and the latter, MDPs, being just P-complete. Hence, current RL algorithms for Dec-POMDPs suffer from poor sample complexity, which greatly reduces their applicability to practical problems where environment interaction is costly. Our key insight is that using just a polynomial number of samples, one can learn a centralized model that generalizes across different policies. We can then optimize the policy within the learned model instead of the true system, without requiring additional environment interactions. We also learn a centralized exploration policy within our model that learns to collect additional data in state-action regions with high model uncertainty. We empirically evaluate the proposed model-based algorithm, MARCO, in three cooperative communication tasks, where it improves sample efficiency by up to 20x. Finally, to investigate the theoretical sample complexity, we adapt an existing model-based method for tabular MDPs to Dec-POMDPs, and prove that it achieves polynomial sample complexity.

Deepak Pathak, Chris Lu, Trevor Darrell et al.

Contemporary sensorimotor learning approaches typically start with an existing complex agent (e.g., a robotic arm), which they learn to control. In contrast, this paper investigates a modular co-evolution strategy: a collection of primitive agents learns to dynamically self-assemble into composite bodies while also learning to coordinate their behavior to control these bodies. Each primitive agent consists of a limb with a motor attached at one end. Limbs may choose to link up to form collectives. When a limb initiates a link-up action, and there is another limb nearby, the latter is magnetically connected to the 'parent' limb's motor. This forms a new single agent, which may further link with other agents. In this way, complex morphologies can emerge, controlled by a policy whose architecture is in explicit correspondence with the morphology. We evaluate the performance of these dynamic and modular agents in simulated environments. We demonstrate better generalization to test-time changes both in the environment, as well as in the structure of the agent, compared to static and monolithic baselines. Project video and code are available at https://pathak22.github.io/modular-assemblies/