Temporally extended actions improve the ability to explore and plan in single-agent settings. In multi-agent settings, the exponential growth of the joint state space with the number of agents makes coordinated behaviours even more valuable. Yet, this same exponential growth renders the design of multi-agent options particularly challenging. Existing multi-agent option discovery methods often sacrifice coordination by producing loosely coupled or fully independent behaviors. Toward addressing these limitations, we describe a novel approach for multi-agent option discovery. Specifically, we propose a joint-state abstraction that compresses the state space while preserving the information necessary to discover strongly coordinated behaviours. Our approach builds on the inductive bias that synchronisation over agent states provides a natural foundation for coordination in the absence of explicit objectives. We first approximate a fictitious state of maximal alignment with the team, the Fermat state, and use it to define a measure of spreadness, capturing team-level misalignment on each individual state dimension. Building on this representation, we then employ a neural graph Laplacian estimator to derive options that capture state synchronisation patterns between agents. We evaluate the resulting options across multiple scenarios in two multi-agent domains, showing that they yield stronger downstream coordination capabilities compared to alternative option discovery methods.

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained since the first time step. We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we introduce an agent that combines DQN and the core ideas of distributional DP, and empirically evaluate it for solving instances of the applications discussed.

Cooperative multi-agent reinforcement learning (MARL) is typically framed as a decentralised partially observable Markov decision process (Dec-POMDP), a setting whose hardness stems from two key challenges: partial observability and decentralised coordination. Genuinely solving such tasks requires Dec-POMDP reasoning, where agents use history to infer hidden states and coordinate based on local information. Yet it remains unclear whether popular benchmarks actually demand this reasoning or permit success via simpler strategies. We introduce a diagnostic suite combining statistically grounded performance comparisons and information-theoretic probes to audit the behavioural complexity of baseline policies (IPPO and MAPPO) across 37 scenarios spanning MPE, SMAX, Overcooked, Hanabi, and MaBrax. Our diagnostics reveal that success on these benchmarks rarely requires genuine Dec-POMDP reasoning. Reactive policies match the performance of memory-based agents in over half the scenarios, and emergent coordination frequently relies on brittle, synchronous action coupling rather than robust temporal influence. These findings suggest that some widely used benchmarks may not adequately test core Dec-POMDP assumptions under current training paradigms, potentially leading to over-optimistic assessments of progress. We release our diagnostic tooling to support more rigorous environment design and evaluation in cooperative MARL.

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

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.

Cooperative multi-agent reinforcement learning (MARL) is typically formalised as a Decentralised Partially Observable Markov Decision Process (Dec-POMDP), where agents must reason about the environment and other agents' behaviour. In practice, current model-free MARL algorithms use simple recurrent function approximators to address the challenge of reasoning about others using partial information. In this position paper, we argue that the empirical success of these methods is not due to effective Markov signal recovery, but rather to learning simple conventions that bypass environment observations and memory. Through a targeted case study, we show that co-adapting agents can learn brittle conventions, which then fail when partnered with non-adaptive agents. Crucially, the same models can learn grounded policies when the task design necessitates it, revealing that the issue is not a fundamental limitation of the learning models but a failure of the benchmark design. Our analysis also suggests that modern MARL environments may not adequately test the core assumptions of Dec-POMDPs. We therefore advocate for new cooperative environments built upon two core principles: (1) behaviours grounded in observations and (2) memory-based reasoning about other agents, ensuring success requires genuine skill rather than fragile, co-adapted agreements.

Are world models a necessary ingredient for flexible, goal-directed behaviour, or is model-free learning sufficient? We provide a formal answer to this question, showing that any agent capable of generalizing to multi-step goal-directed tasks must have learned a predictive model of its environment. We show that this model can be extracted from the agent's policy, and that increasing the agents performance or the complexity of the goals it can achieve requires learning increasingly accurate world models. This has a number of consequences: from developing safe and general agents, to bounding agent capabilities in complex environments, and providing new algorithms for eliciting world models from agents.

Resource constraints can fundamentally change both learning and decision-making. We explore how memory constraints influence an agent's performance when navigating unknown environments using standard reinforcement learning algorithms. Specifically, memory-constrained agents face a dilemma: how much of their limited memory should be allocated to each of the agent's internal processes, such as estimating a world model, as opposed to forming a plan using that model? We study this dilemma in MCTS- and DQN-based algorithms and examine how different allocations of memory impact performance in episodic and continual learning settings.

Extracting relevant information from a stream of high-dimensional observations is a central challenge for deep reinforcement learning agents. Actor-critic algorithms add further complexity to this challenge, as it is often unclear whether the same information will be relevant to both the actor and the critic. To this end, we here explore the principles that underlie effective representations for an actor and for a critic. We focus our study on understanding whether an actor and a critic will benefit from a decoupled, rather than shared, representation. Our primary finding is that when decoupled, the representations for the actor and critic systematically specialise in extracting different types of information from the environment---the actor's representation tends to focus on action-relevant information, while the critic's representation specialises in encoding value and dynamics information. Finally, we demonstrate how these insights help select representation learning objectives that play into the actor's and critic's respective knowledge specialisations, and improve performance in terms of agent returns.

We consider how to construct state abstractions compatible with a given set of abstract actions, to obtain a well-formed abstract Markov decision process (MDP). We show that the Bellman equation suggests that abstract states should represent distributions over states in the ground MDP; we characterize the conditions under which the resulting process is Markov and approximately model-preserving, derive algorithms for constructing and planning with the abstract MDP, and apply them to a visual maze task. We generalize these results to the factored actions case, characterizing the conditions that result in factored abstract states and apply the resulting algorithm to Montezuma's Revenge. These results provide a powerful and principled framework for constructing neurosymbolic abstract Markov decision processes.

Black swan events are statistically rare occurrences that carry extremely high risks. A typical view of defining black swan events is heavily assumed to originate from an unpredictable time-varying environments; however, the community lacks a comprehensive definition of black swan events. To this end, this paper challenges that the standard view is incomplete and claims that high-risk, statistically rare events can also occur in unchanging environments due to human misperception of their value and likelihood, which we call as spatial black swan event. We first carefully categorize black swan events, focusing on spatial black swan events, and mathematically formalize the definition of black swan events. We hope these definitions can pave the way for the development of algorithms to prevent such events by rationally correcting human perception.

Modern reinforcement learning has been conditioned by at least three dogmas. The first is the environment spotlight, which refers to our tendency to focus on modeling environments rather than agents. The second is our treatment of learning as finding the solution to a task, rather than adaptation. The third is the reward hypothesis, which states that all goals and purposes can be well thought of as maximization of a reward signal. These three dogmas shape much of what we think of as the science of reinforcement learning. While each of the dogmas have played an important role in developing the field, it is time we bring them to the surface and reflect on whether they belong as basic ingredients of our scientific paradigm. In order to realize the potential of reinforcement learning as a canonical frame for researching intelligent agents, we suggest that it is time we shed dogmas one and two entirely, and embrace a nuanced approach to the third.

Humans use social context to specify preferences over behaviors, i.e. their reward functions. Yet, algorithms for inferring reward models from preference data do not take this social learning view into account. Inspired by pragmatic human communication, we study how to extract fine-grained data regarding why an example is preferred that is useful for learning more accurate reward models. We propose to enrich binary preference queries to ask both (1) which features of a given example are preferable in addition to (2) comparisons between examples themselves. We derive an approach for learning from these feature-level preferences, both for cases where users specify which features are reward-relevant, and when users do not. We evaluate our approach on linear bandit settings in both vision- and language-based domains. Results support the efficiency of our approach in quickly converging to accurate rewards with fewer comparisons vs. example-only labels. Finally, we validate the real-world applicability with a behavioral experiment on a mushroom foraging task. Our findings suggest that incorporating pragmatic feature preferences is a promising approach for more efficient user-aligned reward learning.

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.

The reward hypothesis posits that, "all of what we mean by goals and purposes can be well thought of as maximization of the expected value of the cumulative sum of a received scalar signal (reward)." We aim to fully settle this hypothesis. This will not conclude with a simple affirmation or refutation, but rather specify completely the implicit requirements on goals and purposes under which the hypothesis holds.

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.

Reward is the driving force for reinforcement-learning agents. We here set out to understand the expressivity of Markov 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": (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 perform each task type, and correctly determine when no such reward function exists.

(Q1) What does it mean for Bob to *solve* one of these tasks? That is, if Alice chooses a SOAP, PO, or TO for Bob to learn to solve, when can Alice determine Bob has solved the task? A: Bob can be said to be doing better on a given task if his behavior improves, as is typical in evaluating behavior under reward. The difference with SOAPs, POs, and TOs is that we measure improvement relative to the task rather than reward. For instance, given a SOAP, we might say that Bob has solved the task once he has found one of the good policies, and we might measure Bob’s progress on a task in terms of the distance of his greedy policy to one of the good policies (as done in our learning experiments). The same reasoning applies to POs and TOs: Bob is doing better on a task in so far as his greedy policy (or trajectories) is (are) higher up the ordering.

One of the most striking features of human cognition is the ability to plan. Two aspects of human planning stand out-its efficiency and flexibility. Efficiency is especially impressive because plans must often be made in complex environments, and yet people successfully plan solutions to many everyday problems despite having limited cognitive resources1-3. Standard accounts in psychology, economics and artificial intelligence have suggested that human planning succeeds because people have a complete representation of a task and then use heuristics to plan future actions in that representation4-11. However, this approach generally assumes that task representations are fixed. Here we propose that task representations can be controlled and that such control provides opportunities to quickly simplify problems and more easily reason about them. We propose a computational account of this simplification process and, in a series of preregistered behavioural experiments, show that it is subject to online cognitive control12-14 and that people optimally balance the complexity of a task representation and its utility for planning and acting. These results demonstrate how strategically perceiving and conceiving problems facilitates the effective use of limited cognitive resources.