Satinder Singh

David Abel, André Barreto, Benjamin Van Roy et al. · deepmind, stanford

In a standard view of the reinforcement learning problem, an agent's goal is to efficiently identify a policy that maximizes long-term reward. However, this perspective is based on a restricted view of learning as finding a solution, rather than treating learning as endless adaptation. In contrast, continual reinforcement learning refers to the setting in which the best agents never stop learning. Despite the importance of continual reinforcement learning, the community lacks a simple definition of the problem that highlights its commitments and makes its primary concepts precise and clear. To this end, this paper is dedicated to carefully defining the continual reinforcement learning problem. We formalize the notion of agents that "never stop learning" through a new mathematical language for analyzing and cataloging agents. Using this new language, we define a continual learning agent as one that can be understood as carrying out an implicit search process indefinitely, and continual reinforcement learning as the setting in which the best agents are all continual learning agents. We provide two motivating examples, illustrating that traditional views of multi-task reinforcement learning and continual supervised learning are special cases of our definition. Collectively, these definitions and perspectives formalize many intuitive concepts at the heart of learning, and open new research pathways surrounding continual learning agents.

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.

David Abel, André Barreto, Hado van Hasselt et al. · deepmind, stanford

When has an agent converged? Standard models of the reinforcement learning problem give rise to a straightforward definition of convergence: An agent converges when its behavior or performance in each environment state stops changing. However, as we shift the focus of our learning problem from the environment's state to the agent's state, the concept of an agent's convergence becomes significantly less clear. In this paper, we propose two complementary accounts of agent convergence in a framing of the reinforcement learning problem that centers around bounded agents. The first view says that a bounded agent has converged when the minimal number of states needed to describe the agent's future behavior cannot decrease. The second view says that a bounded agent has converged just when the agent's performance only changes if the agent's internal state changes. We establish basic properties of these two definitions, show that they accommodate typical views of convergence in standard settings, and prove several facts about their nature and relationship. We take these perspectives, definitions, and analysis to bring clarity to a central idea of the field.

Dilip Arumugam, Satinder Singh · stanford

The Bayes-Adaptive Markov Decision Process (BAMDP) formalism pursues the Bayes-optimal solution to the exploration-exploitation trade-off in reinforcement learning. As the computation of exact solutions to Bayesian reinforcement-learning problems is intractable, much of the literature has focused on developing suitable approximation algorithms. In this work, before diving into algorithm design, we first define, under mild structural assumptions, a complexity measure for BAMDP planning. As efficient exploration in BAMDPs hinges upon the judicious acquisition of information, our complexity measure highlights the worst-case difficulty of gathering information and exhausting epistemic uncertainty. To illustrate its significance, we establish a computationally-intractable, exact planning algorithm that takes advantage of this measure to show more efficient planning. We then conclude by introducing a specific form of state abstraction with the potential to reduce BAMDP complexity and gives rise to a computationally-tractable, approximate planning algorithm.

Julien Perolat, Bart de Vylder, Daniel Hennes et al.

We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling' around it, by directly modifying the underlying multi-agent learning dynamics. DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a yearly (2022) and all-time top-3 rank on the Gravon games platform, competing with human expert players.

Wilka Carvalho, Andre Saraiva, Angelos Filos et al. · deepmind, stanford

The Option Keyboard (OK) was recently proposed as a method for transferring behavioral knowledge across tasks. OK transfers knowledge by adaptively combining subsets of known behaviors using Successor Features (SFs) and Generalized Policy Improvement (GPI). However, it relies on hand-designed state-features and task encodings which are cumbersome to design for every new environment. In this work, we propose the "Successor Features Keyboard" (SFK), which enables transfer with discovered state-features and task encodings. To enable discovery, we propose the "Categorical Successor Feature Approximator" (CSFA), a novel learning algorithm for estimating SFs while jointly discovering state-features and task encodings. With SFK and CSFA, we achieve the first demonstration of transfer with SFs in a challenging 3D environment where all the necessary representations are discovered. We first compare CSFA against other methods for approximating SFs and show that only CSFA discovers representations compatible with SF&GPI at this scale. We then compare SFK against transfer learning baselines and show that it transfers most quickly to long-horizon tasks.

Jelena Luketina, Sebastian Flennerhag, Yannick Schroecker et al. · deepmind

Meta-gradient methods (Xu et al., 2018; Zahavy et al., 2020) offer a promising solution to the problem of hyperparameter selection and adaptation in non-stationary reinforcement learning problems. However, the properties of meta-gradients in such environments have not been systematically studied. In this work, we bring new clarity to meta-gradients in non-stationary environments. Concretely, we ask: (i) how much information should be given to the learned optimizers, so as to enable faster adaptation and generalization over a lifetime, (ii) what meta-optimizer functions are learned in this process, and (iii) whether meta-gradient methods provide a bigger advantage in highly non-stationary environments. To study the effect of information provided to the meta-optimizer, as in recent works (Flennerhag et al., 2021; Almeida et al., 2021), we replace the tuned meta-parameters of fixed update rules with learned meta-parameter functions of selected context features. The context features carry information about agent performance and changes in the environment and hence can inform learned meta-parameter schedules. We find that adding more contextual information is generally beneficial, leading to faster adaptation of meta-parameter values and increased performance over a lifetime. We support these results with a qualitative analysis of resulting meta-parameter schedules and learned functions of context features. Lastly, we find that without context, meta-gradients do not provide a consistent advantage over the baseline in highly non-stationary environments. Our findings suggest that contextualizing meta-gradients can play a pivotal role in extracting high performance from meta-gradients in non-stationary settings.

Tom Zahavy, Vivek Veeriah, Shaobo Hou et al.

In recent years, Artificial Intelligence (AI) systems have surpassed human intelligence in a variety of computational tasks. However, AI systems, like humans, make mistakes, have blind spots, hallucinate, and struggle to generalize to new situations. This work explores whether AI can benefit from creative decision-making mechanisms when pushed to the limits of its computational rationality. In particular, we investigate whether a team of diverse AI systems can outperform a single AI in challenging tasks by generating more ideas as a group and then selecting the best ones. We study this question in the game of chess, the so-called drosophila of AI. We build on AlphaZero (AZ) and extend it to represent a league of agents via a latent-conditioned architecture, which we call AZ_db. We train AZ_db to generate a wider range of ideas using behavioral diversity techniques and select the most promising ones with sub-additive planning. Our experiments suggest that AZ_db plays chess in diverse ways, solves more puzzles as a group and outperforms a more homogeneous team. Notably, AZ_db solves twice as many challenging puzzles as AZ, including the challenging Penrose positions. When playing chess from different openings, we notice that players in AZ_db specialize in different openings, and that selecting a player for each opening using sub-additive planning results in a 50 Elo improvement over AZ. Our findings suggest that diversity bonuses emerge in teams of AI agents, just as they do in teams of humans and that diversity is a valuable asset in solving computationally hard problems.

Michael Laskin, Luyu Wang, Junhyuk Oh et al.

We propose Algorithm Distillation (AD), a method for distilling reinforcement learning (RL) algorithms into neural networks by modeling their training histories with a causal sequence model. Algorithm Distillation treats learning to reinforcement learn as an across-episode sequential prediction problem. A dataset of learning histories is generated by a source RL algorithm, and then a causal transformer is trained by autoregressively predicting actions given their preceding learning histories as context. Unlike sequential policy prediction architectures that distill post-learning or expert sequences, AD is able to improve its policy entirely in-context without updating its network parameters. We demonstrate that AD can reinforcement learn in-context in a variety of environments with sparse rewards, combinatorial task structure, and pixel-based observations, and find that AD learns a more data-efficient RL algorithm than the one that generated the source data.

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.

Ethan Brooks, Logan Walls, Richard L. Lewis et al.

This work presents In-Context Policy Iteration, an algorithm for performing Reinforcement Learning (RL), in-context, using foundation models. While the application of foundation models to RL has received considerable attention, most approaches rely on either (1) the curation of expert demonstrations (either through manual design or task-specific pretraining) or (2) adaptation to the task of interest using gradient methods (either fine-tuning or training of adapter layers). Both of these techniques have drawbacks. Collecting demonstrations is labor-intensive, and algorithms that rely on them do not outperform the experts from which the demonstrations were derived. All gradient techniques are inherently slow, sacrificing the "few-shot" quality that made in-context learning attractive to begin with. In this work, we present an algorithm, ICPI, that learns to perform RL tasks without expert demonstrations or gradients. Instead we present a policy-iteration method in which the prompt content is the entire locus of learning. ICPI iteratively updates the contents of the prompt from which it derives its policy through trial-and-error interaction with an RL environment. In order to eliminate the role of in-weights learning (on which approaches like Decision Transformer rely heavily), we demonstrate our algorithm using Codex, a language model with no prior knowledge of the domains on which we evaluate it.

Tom Zahavy, Yannick Schroecker, Feryal Behbahani et al.

Finding different solutions to the same problem is a key aspect of intelligence associated with creativity and adaptation to novel situations. In reinforcement learning, a set of diverse policies can be useful for exploration, transfer, hierarchy, and robustness. We propose DOMiNO, a method for Diversity Optimization Maintaining Near Optimality. We formalize the problem as a Constrained Markov Decision Process where the objective is to find diverse policies, measured by the distance between the state occupancies of the policies in the set, while remaining near-optimal with respect to the extrinsic reward. We demonstrate that the method can discover diverse and meaningful behaviors in various domains, such as different locomotion patterns in the DeepMind Control Suite. We perform extensive analysis of our approach, compare it with other multi-objective baselines, demonstrate that we can control both the quality and the diversity of the set via interpretable hyperparameters, and show that the discovered set is robust to perturbations.

Ted Moskovitz, Brendan O'Donoghue, Vivek Veeriah et al.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Wilka Carvalho, Angelos Filos, Richard L. Lewis et al.

Recently, the Successor Features and Generalized Policy Improvement (SF&GPI) framework has been proposed as a method for learning, composing, and transferring predictive knowledge and behavior. SF&GPI works by having an agent learn predictive representations (SFs) that can be combined for transfer to new tasks with GPI. However, to be effective this approach requires state features that are useful to predict, and these state-features are typically hand-designed. In this work, we present a novel neural network architecture, "Modular Successor Feature Approximators" (MSFA), where modules both discover what is useful to predict, and learn their own predictive representations. We show that MSFA is able to better generalize compared to baseline architectures for learning SFs and modular architectures

Ali Pourranjbar, Georges Kaddoum, Verdier Assoume Mba et al.

We propose a blind ML-based modulation detection for OFDM-based technologies. Unlike previous works that assume an ideal environment with precise knowledge of subcarrier count and cyclic prefix location, we consider blind modulation detection while accounting for realistic environmental parameters and imperfections. Our approach employs a ResNet network to simultaneously detect the modulation type and accurately locate the cyclic prefix. Specifically, after eliminating the environmental impact from the signal and accurately extracting the OFDM symbols, we convert these symbols into scatter plots. Due to their unique shapes, these scatter plots are then classified using ResNet. As a result, our proposed modulation classification method can be applied to any OFDM-based technology without prior knowledge of the transmitted signal. We evaluate its performance across various modulation schemes and subcarrier numbers. Simulation results show that our method achieves a modulation detection accuracy exceeding $80\%$ at an SNR of $10$ dB and $95\%$ at an SNR of $25$ dB.

Hao Liu, Tom Zahavy, Volodymyr Mnih et al.

Large and diverse datasets have been the cornerstones of many impressive advancements in artificial intelligence. Intelligent creatures, however, learn by interacting with the environment, which changes the input sensory signals and the state of the environment. In this work, we aim to bring the best of both worlds and propose an algorithm that exhibits an exploratory behavior whilst it utilizes large diverse datasets. Our key idea is to leverage deep generative models that are pretrained on static datasets and introduce a dynamic model in the latent space. The transition dynamics simply mixes an action and a random sampled latent. It then applies an exponential moving average for temporal persistency, the resulting latent is decoded to image using pretrained generator. We then employ an unsupervised reinforcement learning algorithm to explore in this environment and perform unsupervised representation learning on the collected data. We further leverage the temporal information of this data to pair data points as a natural supervision for representation learning. Our experiments suggest that the learned representations can be successfully transferred to downstream tasks in both vision and reinforcement learning domains.

Sebastian Flennerhag, Tom Zahavy, Brendan O'Donoghue et al.

We study the connection between gradient-based meta-learning and convex op-timisation. We observe that gradient descent with momentum is a special case of meta-gradients, and building on recent results in optimisation, we prove convergence rates for meta-learning in the single task setting. While a meta-learned update rule can yield faster convergence up to constant factor, it is not sufficient for acceleration. Instead, some form of optimism is required. We show that optimism in meta-learning can be captured through Bootstrapped Meta-Gradients (Flennerhag et al., 2022), providing deeper insight into its underlying mechanics.

Bernardo Avila Pires, Feryal Behbahani, Hubert Soyer et al.

Hierarchical Reinforcement Learning (HRL) agents have the potential to demonstrate appealing capabilities such as planning and exploration with abstraction, transfer, and skill reuse. Recent successes with HRL across different domains provide evidence that practical, effective HRL agents are possible, even if existing agents do not yet fully realize the potential of HRL. Despite these successes, visually complex partially observable 3D environments remained a challenge for HRL agents. We address this issue with Hierarchical Hybrid Offline-Online (H2O2), a hierarchical deep reinforcement learning agent that discovers and learns to use options from scratch using its own experience. We show that H2O2 is competitive with a strong non-hierarchical Muesli baseline in the DeepMind Hard Eight tasks and we shed new light on the problem of learning hierarchical agents in complex environments. Our empirical study of H2O2 reveals previously unnoticed practical challenges and brings new perspective to the current understanding of hierarchical agents in complex domains.

Khimya Khetarpal, Claire Vernade, Brendan O'Donoghue et al.

We study the problem of planning under model uncertainty in an online meta-reinforcement learning (RL) setting where an agent is presented with a sequence of related tasks with limited interactions per task. The agent can use its experience in each task and across tasks to estimate both the transition model and the distribution over tasks. We propose an algorithm to meta-learn the underlying structure across tasks, utilize it to plan in each task, and upper-bound the regret of the planning loss. Our bound suggests that the average regret over tasks decreases as the number of tasks increases and as the tasks are more similar. In the classical single-task setting, it is known that the planning horizon should depend on the estimated model's accuracy, that is, on the number of samples within task. We generalize this finding to meta-RL and study this dependence of planning horizons on the number of tasks. Based on our theoretical findings, we derive heuristics for selecting slowly increasing discount factors, and we validate its significance empirically.

Jake Bruce, Michael Dennis, Ashley Edwards et al. · oxford

We introduce Genie, the first generative interactive environment trained in an unsupervised manner from unlabelled Internet videos. The model can be prompted to generate an endless variety of action-controllable virtual worlds described through text, synthetic images, photographs, and even sketches. At 11B parameters, Genie can be considered a foundation world model. It is comprised of a spatiotemporal video tokenizer, an autoregressive dynamics model, and a simple and scalable latent action model. Genie enables users to act in the generated environments on a frame-by-frame basis despite training without any ground-truth action labels or other domain-specific requirements typically found in the world model literature. Further the resulting learned latent action space facilitates training agents to imitate behaviors from unseen videos, opening the path for training generalist agents of the future.

Zeyu Zheng, Vivek Veeriah, Risto Vuorio et al.

Our main contribution in this work is an empirical finding that random General Value Functions (GVFs), i.e., deep action-conditional predictions -- random both in what feature of observations they predict as well as in the sequence of actions the predictions are conditioned upon -- form good auxiliary tasks for reinforcement learning (RL) problems. In particular, we show that random deep action-conditional predictions when used as auxiliary tasks yield state representations that produce control performance competitive with state-of-the-art hand-crafted auxiliary tasks like value prediction, pixel control, and CURL in both Atari and DeepMind Lab tasks. In another set of experiments we stop the gradients from the RL part of the network to the state representation learning part of the network and show, perhaps surprisingly, that the auxiliary tasks alone are sufficient to learn state representations good enough to outperform an end-to-end trained actor-critic baseline. We opensourced our code at https://github.com/Hwhitetooth/random_gvfs.

Ian Osband, Yotam Doron, Matteo Hessel et al.

This paper introduces the Behaviour Suite for Reinforcement Learning, or bsuite for short. bsuite is a collection of carefully-designed experiments that investigate core capabilities of reinforcement learning (RL) agents with two objectives. First, to collect clear, informative and scalable problems that capture key issues in the design of general and efficient learning algorithms. Second, to study agent behaviour through their performance on these shared benchmarks. To complement this effort, we open source github.com/deepmind/bsuite, which automates evaluation and analysis of any agent on bsuite. This library facilitates reproducible and accessible research on the core issues in RL, and ultimately the design of superior learning algorithms. Our code is Python, and easy to use within existing projects. We include examples with OpenAI Baselines, Dopamine as well as new reference implementations. Going forward, we hope to incorporate more excellent experiments from the research community, and commit to a periodic review of bsuite from a committee of prominent researchers.

Janarthanan Rajendran, Jatin Ganhotra, Xiaoxiao Guo et al.

Many Natural Language Processing (NLP) tasks depend on using Named Entities (NEs) that are contained in texts and in external knowledge sources. While this is easy for humans, the present neural methods that rely on learned word embeddings may not perform well for these NLP tasks, especially in the presence of Out-Of-Vocabulary (OOV) or rare NEs. In this paper, we propose a solution for this problem, and present empirical evaluations on: a) a structured Question-Answering task, b) three related Goal-Oriented dialog tasks, and c) a Reading-Comprehension task, which show that the proposed method can be effective in dealing with both in-vocabulary and OOV NEs. We create extended versions of dialog bAbI tasks 1,2 and 4 and OOV versions of the CBT test set available at - https://github.com/IBM/ne-table-datasets.

John Schultz, Jakub Adamek, Matej Jusup et al. · deepmind

Advancing planning and reasoning capabilities of Large Language Models (LLMs) is one of the key prerequisites towards unlocking their potential for performing reliably in complex and impactful domains. In this paper, we aim to demonstrate this across board games (Chess, Fischer Random / Chess960, Connect Four, and Hex), and we show that search-based planning can yield significant improvements in LLM game-playing strength. We introduce, compare and contrast two major approaches: In external search, the model guides Monte Carlo Tree Search (MCTS) rollouts and evaluations without calls to an external game engine, and in internal search, the model is trained to generate in-context a linearized tree of search and a resulting final choice. Both build on a language model pre-trained on relevant domain knowledge, reliably capturing the transition and value functions in the respective environments, with minimal hallucinations. We evaluate our LLM search implementations against game-specific state-of-the-art engines, showcasing substantial improvements in strength over the base model, and reaching Grandmaster-level performance in chess while operating closer to the human search budget. Our proposed approach, combining search with domain knowledge, is not specific to board games, hinting at more general future applications.

David Abel, André Barreto, Michael Bowling et al. · deepmind

Agency is a system's capacity to steer outcomes toward a goal, and is a central topic of study across biology, philosophy, cognitive science, and artificial intelligence. Determining if a system exhibits agency is a notoriously difficult question: Dennett (1989), for instance, highlights the puzzle of determining which principles can decide whether a rock, a thermostat, or a robot each possess agency. We here address this puzzle from the viewpoint of reinforcement learning by arguing that agency is fundamentally frame-dependent: Any measurement of a system's agency must be made relative to a reference frame. We support this claim by presenting a philosophical argument that each of the essential properties of agency proposed by Barandiaran et al. (2009) and Moreno (2018) are themselves frame-dependent. We conclude that any basic science of agency requires frame-dependence, and discuss the implications of this claim for reinforcement learning.

David Abel, Michael Bowling, André Barreto et al. · deepmind

Agents are minimally entities that are influenced by their past observations and act to influence future observations. This latter capacity is captured by empowerment, which has served as a vital framing concept across artificial intelligence and cognitive science. This former capacity, however, is equally foundational: In what ways, and to what extent, can an agent be influenced by what it observes? In this paper, we ground this concept in a universal agent-centric measure that we refer to as plasticity, and reveal a fundamental connection to empowerment. Following a set of desiderata on a suitable definition, we define plasticity using a new information-theoretic quantity we call the generalized directed information. We show that this new quantity strictly generalizes the directed information introduced by Massey (1990) while preserving all of its desirable properties. Under this definition, we find that plasticity is well thought of as the mirror of empowerment: The two concepts are defined using the same measure, with only the direction of influence reversed. Our main result establishes a tension between the plasticity and empowerment of an agent, suggesting that agent design needs to be mindful of both characteristics. We explore the implications of these findings, and suggest that plasticity, empowerment, and their relationship are essential to understanding agency

Xidong Feng, Vivek Veeriah, Marcus Chiam et al.

While Generative AI rapidly advances in various domains, generating truly creative, aesthetic, and counter-intuitive outputs remains a challenge. This paper presents an approach to tackle these difficulties in the domain of chess puzzles. We start by benchmarking Generative AI architectures, and then introduce an RL framework with novel rewards based on chess engine search statistics to overcome some of those shortcomings. The rewards are designed to enhance a puzzle's uniqueness, counter-intuitiveness, diversity, and realism. Our RL approach dramatically increases counter-intuitive puzzle generation by 10x, from 0.22\% (supervised) to 2.5\%, surpassing existing dataset rates (2.1\%) and the best Lichess-trained model (0.4\%). Our puzzles meet novelty and diversity benchmarks, retain aesthetic themes, and are rated by human experts as more creative, enjoyable, and counter-intuitive than composed book puzzles, even approaching classic compositions. Our final outcome is a curated booklet of these AI-generated puzzles, which is acknowledged for creativity by three world-renowned experts.

Vivek Veeriah, Federico Barbero, Marcus Chiam et al.

The rapid advancement of Generative AI has raised significant questions regarding its ability to produce creative and novel outputs. Our recent work investigates this question within the domain of chess puzzles and presents an AI system designed to generate puzzles characterized by aesthetic appeal, novelty, counter-intuitive and unique solutions. We briefly discuss our method below and refer the reader to the technical paper for more details. To assess our system's creativity, we presented a curated booklet of AI-generated puzzles to three world-renowned experts: International Master for chess compositions Amatzia Avni, Grandmaster Jonathan Levitt, and Grandmaster Matthew Sadler. All three are noted authors on chess aesthetics and the evolving role of computers in the game. They were asked to select their favorites and explain what made them appealing, considering qualities such as their creativity, level of challenge, or aesthetic design.

Wolfgang Lehrach, Daniel Hennes, Miguel Lazaro-Gredilla et al.

Large Language Models (LLMs) reasoning abilities are increasingly being applied to classical board and card games, but the dominant approach -- involving prompting for direct move generation -- has significant drawbacks. It relies on the model's implicit fragile pattern-matching capabilities, leading to frequent illegal moves and strategically shallow play. Here we introduce an alternative approach: We use the LLM to translate natural language rules and game trajectories into a formal, executable world model represented as Python code. This generated model -- comprising functions for state transition, legal move enumeration, and termination checks -- serves as a verifiable simulation engine for high-performance planning algorithms like Monte Carlo tree search (MCTS). In addition, we prompt the LLM to generate heuristic value functions (to make MCTS more efficient), and inference functions (to estimate hidden states in imperfect information games). Our method offers three distinct advantages compared to directly using the LLM as a policy: (1) Verifiability: The generated CWM serves as a formal specification of the game's rules, allowing planners to algorithmically enumerate valid actions and avoid illegal moves, contingent on the correctness of the synthesized model; (2) Strategic Depth: We combine LLM semantic understanding with the deep search power of classical planners; and (3) Generalization: We direct the LLM to focus on the meta-task of data-to-code translation, enabling it to adapt to new games more easily. We evaluate our agent on 10 different games, of which 4 are novel and created for this paper. 5 of the games are fully observed (perfect information), and 5 are partially observed (imperfect information). We find that our method outperforms or matches Gemini 2.5 Pro in 9 out of the 10 considered games.

Zheng Wen, Doina Precup, Benjamin Van Roy et al.

Any agents we can possibly build are subject to capacity constraints, as memory and compute resources are inherently finite. However, comparatively little attention has been dedicated to understanding how agents with limited capacity should allocate their resources for optimal performance. The goal of this paper is to shed some light on this question by studying a simple yet relevant continual learning problem: the capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem. We derive a solution to this problem under appropriate technical conditions. Moreover, for problems that can be decomposed into a set of sub-problems, we also demonstrate how to optimally allocate capacity across these sub-problems in the steady state. We view the results of this paper as a first step in the systematic theoretical study of learning under capacity constraints.

Vivek Veeriah, Zeyu Zheng, Richard Lewis et al.

Planning with a learned model is arguably a key component of intelligence. There are several challenges in realizing such a component in large-scale reinforcement learning (RL) problems. One such challenge is dealing effectively with continuous action spaces when using tree-search planning (e.g., it is not feasible to consider every action even at just the root node of the tree). In this paper we present a method for selecting affordances useful for planning -- for learning which small number of actions/options from a continuous space of actions/options to consider in the tree-expansion process during planning. We consider affordances that are goal-and-state-conditional mappings to actions/options as well as unconditional affordances that simply select actions/options available in all states. Our selection method is gradient based: we compute gradients through the planning procedure to update the parameters of the function that represents affordances. Our empirical work shows that it is feasible to learn to select both primitive-action and option affordances, and that simultaneously learning to select affordances and planning with a learned value-equivalent model can outperform model-free RL.

David Abel, Will Dabney, Anna Harutyunyan et al.

Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of "task" that might be desirable: (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.

Janarthanan Rajendran, Jonathan K. Kummerfeld, Satinder Singh

For each goal-oriented dialog task of interest, large amounts of data need to be collected for end-to-end learning of a neural dialog system. Collecting that data is a costly and time-consuming process. Instead, we show that we can use only a small amount of data, supplemented with data from a related dialog task. Naively learning from related data fails to improve performance as the related data can be inconsistent with the target task. We describe a meta-learning based method that selectively learns from the related dialog task data. Our approach leads to significant accuracy improvements in an example dialog task.

Sebastian Flennerhag, Yannick Schroecker, Tom Zahavy et al.

Meta-learning empowers artificial intelligence to increase its efficiency by learning how to learn. Unlocking this potential involves overcoming a challenging meta-optimisation problem. We propose an algorithm that tackles this problem by letting the meta-learner teach itself. The algorithm first bootstraps a target from the meta-learner, then optimises the meta-learner by minimising the distance to that target under a chosen (pseudo-)metric. Focusing on meta-learning with gradients, we establish conditions that guarantee performance improvements and show that the metric can control meta-optimisation. Meanwhile, the bootstrapping mechanism can extend the effective meta-learning horizon without requiring backpropagation through all updates. We achieve a new state-of-the art for model-free agents on the Atari ALE benchmark and demonstrate that it yields both performance and efficiency gains in multi-task meta-learning. Finally, we explore how bootstrapping opens up new possibilities and find that it can meta-learn efficient exploration in an epsilon-greedy Q-learning agent, without backpropagating through the update rule.

Christopher Grimm, André Barreto, Gregory Farquhar et al.

One of the main challenges in model-based reinforcement learning (RL) is to decide which aspects of the environment should be modeled. The value-equivalence (VE) principle proposes a simple answer to this question: a model should capture the aspects of the environment that are relevant for value-based planning. Technically, VE distinguishes models based on a set of policies and a set of functions: a model is said to be VE to the environment if the Bellman operators it induces for the policies yield the correct result when applied to the functions. As the number of policies and functions increase, the set of VE models shrinks, eventually collapsing to a single point corresponding to a perfect model. A fundamental question underlying the VE principle is thus how to select the smallest sets of policies and functions that are sufficient for planning. In this paper we take an important step towards answering this question. We start by generalizing the concept of VE to order-$k$ counterparts defined with respect to $k$ applications of the Bellman operator. This leads to a family of VE classes that increase in size as $k \rightarrow \infty$. In the limit, all functions become value functions, and we have a special instantiation of VE which we call proper VE or simply PVE. Unlike VE, the PVE class may contain multiple models even in the limit when all value functions are used. Crucially, all these models are sufficient for planning, meaning that they will yield an optimal policy despite the fact that they may ignore many aspects of the environment. We construct a loss function for learning PVE models and argue that popular algorithms such as MuZero can be understood as minimizing an upper bound for this loss. We leverage this connection to propose a modification to MuZero and show that it can lead to improved performance in practice.

Tom Zahavy, Brendan O'Donoghue, Andre Barreto et al.

Finding different solutions to the same problem is a key aspect of intelligence associated with creativity and adaptation to novel situations. In reinforcement learning, a set of diverse policies can be useful for exploration, transfer, hierarchy, and robustness. We propose Diverse Successive Policies, a method for discovering policies that are diverse in the space of Successor Features, while assuring that they are near optimal. We formalize the problem as a Constrained Markov Decision Process (CMDP) where the goal is to find policies that maximize diversity, characterized by an intrinsic diversity reward, while remaining near-optimal with respect to the extrinsic reward of the MDP. We also analyze how recently proposed robustness and discrimination rewards perform and find that they are sensitive to the initialization of the procedure and may converge to sub-optimal solutions. To alleviate this, we propose new explicit diversity rewards that aim to minimize the correlation between the Successor Features of the policies in the set. We compare the different diversity mechanisms in the DeepMind Control Suite and find that the type of explicit diversity we are proposing is important to discover distinct behavior, like for example different locomotion patterns.

Tom Zahavy, Brendan O'Donoghue, Guillaume Desjardins et al.

Maximising a cumulative reward function that is Markov and stationary, i.e., defined over state-action pairs and independent of time, is sufficient to capture many kinds of goals in a Markov decision process (MDP). However, not all goals can be captured in this manner. In this paper we study convex MDPs in which goals are expressed as convex functions of the stationary distribution and show that they cannot be formulated using stationary reward functions. Convex MDPs generalize the standard reinforcement learning (RL) problem formulation to a larger framework that includes many supervised and unsupervised RL problems, such as apprenticeship learning, constrained MDPs, and so-called `pure exploration'. Our approach is to reformulate the convex MDP problem as a min-max game involving policy and cost (negative reward) `players', using Fenchel duality. We propose a meta-algorithm for solving this problem and show that it unifies many existing algorithms in the literature.

Ethan A. Brooks, Janarthanan Rajendran, Richard L. Lewis et al.

Learning to flexibly follow task instructions in dynamic environments poses interesting challenges for reinforcement learning agents. We focus here on the problem of learning control flow that deviates from a strict step-by-step execution of instructions -- that is, control flow that may skip forward over parts of the instructions or return backward to previously completed or skipped steps. Demand for such flexible control arises in two fundamental ways: explicitly when control is specified in the instructions themselves (such as conditional branching and looping) and implicitly when stochastic environment dynamics require re-completion of instructions whose effects have been perturbed, or opportunistic skipping of instructions whose effects are already present. We formulate an attention-based architecture that meets these challenges by learning, from task reward only, to flexibly attend to and condition behavior on an internal encoding of the instructions. We test the architecture's ability to learn both explicit and implicit control in two illustrative domains -- one inspired by Minecraft and the other by StarCraft -- and show that the architecture exhibits zero-shot generalization to novel instructions of length greater than those in a training set, at a performance level unmatched by two baseline recurrent architectures and one ablation architecture.

Vivek Veeriah, Tom Zahavy, Matteo Hessel et al.

Temporal abstractions in the form of options have been shown to help reinforcement learning (RL) agents learn faster. However, despite prior work on this topic, the problem of discovering options through interaction with an environment remains a challenge. In this paper, we introduce a novel meta-gradient approach for discovering useful options in multi-task RL environments. Our approach is based on a manager-worker decomposition of the RL agent, in which a manager maximises rewards from the environment by learning a task-dependent policy over both a set of task-independent discovered-options and primitive actions. The option-reward and termination functions that define a subgoal for each option are parameterised as neural networks and trained via meta-gradients to maximise their usefulness. Empirical analysis on gridworld and DeepMind Lab tasks show that: (1) our approach can discover meaningful and diverse temporally-extended options in multi-task RL domains, (2) the discovered options are frequently used by the agent while learning to solve the training tasks, and (3) that the discovered options help a randomly initialised manager learn faster in completely new tasks.

Zeyu Zheng, Risto Vuorio, Richard Lewis et al.

How much credit (or blame) should an action taken in a state get for a future reward? This is the fundamental temporal credit assignment problem in Reinforcement Learning (RL). One of the earliest and still most widely used heuristics is to assign this credit based on a scalar coefficient, $λ$ (treated as a hyperparameter), raised to the power of the time interval between the state-action and the reward. In this empirical paper, we explore heuristics based on more general pairwise weightings that are functions of the state in which the action was taken, the state at the time of the reward, as well as the time interval between the two. Of course it isn't clear what these pairwise weight functions should be, and because they are too complex to be treated as hyperparameters we develop a metagradient procedure for learning these weight functions during the usual RL training of a policy. Our empirical work shows that it is often possible to learn these pairwise weight functions during learning of the policy to achieve better performance than competing approaches.

Tom Zahavy, Andre Barreto, Daniel J Mankowitz et al.

We study the problem of how to construct a set of policies that can be composed together to solve a collection of reinforcement learning tasks. Each task is a different reward function defined as a linear combination of known features. We consider a specific class of policy compositions which we call set improving policies (SIPs): given a set of policies and a set of tasks, a SIP is any composition of the former whose performance is at least as good as that of its constituents across all the tasks. We focus on the most conservative instantiation of SIPs, set-max policies (SMPs), so our analysis extends to any SIP. This includes known policy-composition operators like generalized policy improvement. Our main contribution is a policy iteration algorithm that builds a set of policies in order to maximize the worst-case performance of the resulting SMP on the set of tasks. The algorithm works by successively adding new policies to the set. We show that the worst-case performance of the resulting SMP strictly improves at each iteration, and the algorithm only stops when there does not exist a policy that leads to improved performance. We empirically evaluate our algorithm on a grid world and also on a set of domains from the DeepMind control suite. We confirm our theoretical results regarding the monotonically improving performance of our algorithm. Interestingly, we also show empirically that the sets of policies computed by the algorithm are diverse, leading to different trajectories in the grid world and very distinct locomotion skills in the control suite.

Qi Zhang, Edmund H. Durfee, Satinder Singh

Multiagent systems can use commitments as the core of a general coordination infrastructure, supporting both cooperative and non-cooperative interactions. Agents whose objectives are aligned, and where one agent can help another achieve greater reward by sacrificing some of its own reward, should choose a cooperative commitment to maximize their joint reward. We present a solution to the problem of how cooperative agents can efficiently find an (approximately) optimal commitment by querying about carefully-selected commitment choices. We prove structural properties of the agents' values as functions of the parameters of the commitment specification, and develop a greedy method for composing a query with provable approximation bounds, which we empirically show can find nearly optimal commitments in a fraction of the time methods that lack our insights require.

Christopher Grimm, André Barreto, Satinder Singh et al.

Learning models of the environment from data is often viewed as an essential component to building intelligent reinforcement learning (RL) agents. The common practice is to separate the learning of the model from its use, by constructing a model of the environment's dynamics that correctly predicts the observed state transitions. In this paper we argue that the limited representational resources of model-based RL agents are better used to build models that are directly useful for value-based planning. As our main contribution, we introduce the principle of value equivalence: two models are value equivalent with respect to a set of functions and policies if they yield the same Bellman updates. We propose a formulation of the model learning problem based on the value equivalence principle and analyze how the set of feasible solutions is impacted by the choice of policies and functions. Specifically, we show that, as we augment the set of policies and functions considered, the class of value equivalent models shrinks, until eventually collapsing to a single point corresponding to a model that perfectly describes the environment. In many problems, directly modelling state-to-state transitions may be both difficult and unnecessary. By leveraging the value-equivalence principle one may find simpler models without compromising performance, saving computation and memory. We illustrate the benefits of value-equivalent model learning with experiments comparing it against more traditional counterparts like maximum likelihood estimation. More generally, we argue that the principle of value equivalence underlies a number of recent empirical successes in RL, such as Value Iteration Networks, the Predictron, Value Prediction Networks, TreeQN, and MuZero, and provides a first theoretical underpinning of those results.

Wilka Carvalho, Anthony Liang, Kimin Lee et al.

First-person object-interaction tasks in high-fidelity, 3D, simulated environments such as the AI2Thor virtual home-environment pose significant sample-efficiency challenges for reinforcement learning (RL) agents learning from sparse task rewards. To alleviate these challenges, prior work has provided extensive supervision via a combination of reward-shaping, ground-truth object-information, and expert demonstrations. In this work, we show that one can learn object-interaction tasks from scratch without supervision by learning an attentive object-model as an auxiliary task during task learning with an object-centric relational RL agent. Our key insight is that learning an object-model that incorporates object-attention into forward prediction provides a dense learning signal for unsupervised representation learning of both objects and their relationships. This, in turn, enables faster policy learning for an object-centric relational RL agent. We demonstrate our agent by introducing a set of challenging object-interaction tasks in the AI2Thor environment where learning with our attentive object-model is key to strong performance. Specifically, we compare our agent and relational RL agents with alternative auxiliary tasks to a relational RL agent equipped with ground-truth object-information, and show that learning with our object-model best closes the performance gap in terms of both learning speed and maximum success rate. Additionally, we find that incorporating object-attention into an object-model's forward predictions is key to learning representations which capture object-category and object-state.

Junhyuk Oh, Matteo Hessel, Wojciech M. Czarnecki et al.

Reinforcement learning (RL) algorithms update an agent's parameters according to one of several possible rules, discovered manually through years of research. Automating the discovery of update rules from data could lead to more efficient algorithms, or algorithms that are better adapted to specific environments. Although there have been prior attempts at addressing this significant scientific challenge, it remains an open question whether it is feasible to discover alternatives to fundamental concepts of RL such as value functions and temporal-difference learning. This paper introduces a new meta-learning approach that discovers an entire update rule which includes both 'what to predict' (e.g. value functions) and 'how to learn from it' (e.g. bootstrapping) by interacting with a set of environments. The output of this method is an RL algorithm that we call Learned Policy Gradient (LPG). Empirical results show that our method discovers its own alternative to the concept of value functions. Furthermore it discovers a bootstrapping mechanism to maintain and use its predictions. Surprisingly, when trained solely on toy environments, LPG generalises effectively to complex Atari games and achieves non-trivial performance. This shows the potential to discover general RL algorithms from data.

Zhongwen Xu, Hado van Hasselt, Matteo Hessel et al.

Deep reinforcement learning includes a broad family of algorithms that parameterise an internal representation, such as a value function or policy, by a deep neural network. Each algorithm optimises its parameters with respect to an objective, such as Q-learning or policy gradient, that defines its semantics. In this work, we propose an algorithm based on meta-gradient descent that discovers its own objective, flexibly parameterised by a deep neural network, solely from interactive experience with its environment. Over time, this allows the agent to learn how to learn increasingly effectively. Furthermore, because the objective is discovered online, it can adapt to changes over time. We demonstrate that the algorithm discovers how to address several important issues in RL, such as bootstrapping, non-stationarity, and off-policy learning. On the Atari Learning Environment, the meta-gradient algorithm adapts over time to learn with greater efficiency, eventually outperforming the median score of a strong actor-critic baseline.

Thomas Anthony, Tom Eccles, Andrea Tacchetti et al.

Recent advances in deep reinforcement learning (RL) have led to considerable progress in many 2-player zero-sum games, such as Go, Poker and Starcraft. The purely adversarial nature of such games allows for conceptually simple and principled application of RL methods. However real-world settings are many-agent, and agent interactions are complex mixtures of common-interest and competitive aspects. We consider Diplomacy, a 7-player board game designed to accentuate dilemmas resulting from many-agent interactions. It also features a large combinatorial action space and simultaneous moves, which are challenging for RL algorithms. We propose a simple yet effective approximate best response operator, designed to handle large combinatorial action spaces and simultaneous moves. We also introduce a family of policy iteration methods that approximate fictitious play. With these methods, we successfully apply RL to Diplomacy: we show that our agents convincingly outperform the previous state-of-the-art, and game theoretic equilibrium analysis shows that the new process yields consistent improvements.

Tom Zahavy, Zhongwen Xu, Vivek Veeriah et al.

Reinforcement learning algorithms are highly sensitive to the choice of hyperparameters, typically requiring significant manual effort to identify hyperparameters that perform well on a new domain. In this paper, we take a step towards addressing this issue by using metagradients to automatically adapt hyperparameters online by meta-gradient descent (Xu et al., 2018). We apply our algorithm, Self-Tuning Actor-Critic (STAC), to self-tune all the differentiable hyperparameters of an actor-critic loss function, to discover auxiliary tasks, and to improve off-policy learning using a novel leaky V-trace operator. STAC is simple to use, sample efficient and does not require a significant increase in compute. Ablative studies show that the overall performance of STAC improved as we adapt more hyperparameters. When applied to the Arcade Learning Environment (Bellemare et al. 2012), STAC improved the median human normalized score in 200M steps from 243% to 364%. When applied to the DM Control suite (Tassa et al., 2018), STAC improved the mean score in 30M steps from 217 to 389 when learning with features, from 108 to 202 when learning from pixels, and from 195 to 295 in the Real-World Reinforcement Learning Challenge (Dulac-Arnold et al., 2020).

Janarthanan Rajendran, Richard Lewis, Vivek Veeriah et al.

We present a method for learning intrinsic reward functions to drive the learning of an agent during periods of practice in which extrinsic task rewards are not available. During practice, the environment may differ from the one available for training and evaluation with extrinsic rewards. We refer to this setup of alternating periods of practice and objective evaluation as practice-match, drawing an analogy to regimes of skill acquisition common for humans in sports and games. The agent must effectively use periods in the practice environment so that performance improves during matches. In the proposed method the intrinsic practice reward is learned through a meta-gradient approach that adapts the practice reward parameters to reduce the extrinsic match reward loss computed from matches. We illustrate the method on a simple grid world, and evaluate it in two games in which the practice environment differs from match: Pong with practice against a wall without an opponent, and PacMan with practice in a maze without ghosts. The results show gains from learning in practice in addition to match periods over learning in matches only.

Zeyu Zheng, Junhyuk Oh, Matteo Hessel et al.

The objective of a reinforcement learning agent is to behave so as to maximise the sum of a suitable scalar function of state: the reward. These rewards are typically given and immutable. In this paper, we instead consider the proposition that the reward function itself can be a good locus of learned knowledge. To investigate this, we propose a scalable meta-gradient framework for learning useful intrinsic reward functions across multiple lifetimes of experience. Through several proof-of-concept experiments, we show that it is feasible to learn and capture knowledge about long-term exploration and exploitation into a reward function. Furthermore, we show that unlike policy transfer methods that capture "how" the agent should behave, the learned reward functions can generalise to other kinds of agents and to changes in the dynamics of the environment by capturing "what" the agent should strive to do.