Michael Wooldridge

Lewis Hammond, James Fox, Tom Everitt et al. · deepmind

Causal reasoning and game-theoretic reasoning are fundamental topics in artificial intelligence, among many other disciplines: this paper is concerned with their intersection. Despite their importance, a formal framework that supports both these forms of reasoning has, until now, been lacking. We offer a solution in the form of (structural) causal games, which can be seen as extending Pearl's causal hierarchy to the game-theoretic domain, or as extending Koller and Milch's multi-agent influence diagrams to the causal domain. We then consider three key questions: i) How can the (causal) dependencies in games - either between variables, or between strategies - be modelled in a uniform, principled manner? ii) How may causal queries be computed in causal games, and what assumptions does this require? iii) How do causal games compare to existing formalisms? To address question i), we introduce mechanised games, which encode dependencies between agents' decision rules and the distributions governing the game. In response to question ii), we present definitions of predictions, interventions, and counterfactuals, and discuss the assumptions required for each. Regarding question iii), we describe correspondences between causal games and other formalisms, and explain how causal games can be used to answer queries that other causal or game-theoretic models do not support. Finally, we highlight possible applications of causal games, aided by an extensive open-source Python library.

Emanuele La Malfa, Aleksandar Petrov, Simon Frieder et al. · oxford

Some of the most powerful language models currently are proprietary systems, accessible only via (typically restrictive) web or software programming interfaces. This is the Language-Models-as-a-Service (LMaaS) paradigm. In contrast with scenarios where full model access is available, as in the case of open-source models, such closed-off language models present specific challenges for evaluating, benchmarking, and testing them. This paper has two goals: on the one hand, we delineate how the aforementioned challenges act as impediments to the accessibility, replicability, reliability, and trustworthiness of LMaaS. We systematically examine the issues that arise from a lack of information about language models for each of these four aspects. We conduct a detailed analysis of existing solutions and put forth a number of considered recommendations, and highlight the directions for future advancements. On the other hand, it serves as a comprehensive resource for existing knowledge on current, major LMaaS, offering a synthesized overview of the licences and capabilities their interfaces offer.

Sanjay Chawla, Preslav Nakov, Ahmed Ali et al. · berkeley

It is ten years since neural networks made their spectacular comeback. Prompted by this anniversary, we take a holistic perspective on Artificial Intelligence (AI). Supervised Learning for cognitive tasks is effectively solved - provided we have enough high-quality labeled data. However, deep neural network models are not easily interpretable, and thus the debate between blackbox and whitebox modeling has come to the fore. The rise of attention networks, self-supervised learning, generative modeling, and graph neural networks has widened the application space of AI. Deep Learning has also propelled the return of reinforcement learning as a core building block of autonomous decision making systems. The possible harms made possible by new AI technologies have raised socio-technical issues such as transparency, fairness, and accountability. The dominance of AI by Big-Tech who control talent, computing resources, and most importantly, data may lead to an extreme AI divide. Failure to meet high expectations in high profile, and much heralded flagship projects like self-driving vehicles could trigger another AI winter.

Jonathan Shaki, Sarit Kraus, Michael Wooldridge

Large Language Models (LLMs) such as ChatGPT have received enormous attention over the past year and are now used by hundreds of millions of people every day. The rapid adoption of this technology naturally raises questions about the possible biases such models might exhibit. In this work, we tested one of these models (GPT-3) on a range of cognitive effects, which are systematic patterns that are usually found in human cognitive tasks. We found that LLMs are indeed prone to several human cognitive effects. Specifically, we show that the priming, distance, SNARC, and size congruity effects were presented with GPT-3, while the anchoring effect is absent. We describe our methodology, and specifically the way we converted real-world experiments to text-based experiments. Finally, we speculate on the possible reasons why GPT-3 exhibits these effects and discuss whether they are imitated or reinvented.

Julian Gutierrez, Muhammad Najib, Giuseppe Perelli et al.

Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium. Rational verification can be understood as a counterpart to model checking for multiagent systems, but while classical model checking can be done in polynomial time for some temporal logic specification languages such as CTL, and polynomial space with LTL specifications, rational verification is much harder: the key decision problems for rational verification are 2EXPTIME-complete with LTL specifications, even when using explicit-state system representations. Against this background, our contributions in this paper are threefold. First, we show that the complexity of rational verification can be greatly reduced by restricting specifications to GR(1), a fragment of LTL that can represent a broad and practically useful class of response properties of reactive systems. In particular, we show that for a number of relevant settings, rational verification can be done in polynomial space and even in polynomial time. Second, we provide improved complexity results for rational verification when considering players' goals given by mean-payoff utility functions; arguably the most widely used approach for quantitative objectives in concurrent and multiagent systems. Finally, we consider the problem of computing outcomes that satisfy social welfare constraints. To this end, we consider both utilitarian and egalitarian social welfare and show that computing such outcomes is either PSPACE-complete or NP-complete.

Arnau Quera-Bofarull, Joel Dyer, Anisoara Calinescu et al.

Agent-based models (ABMs) are a promising approach to modelling and reasoning about complex systems, yet their application in practice is impeded by their complexity, discrete nature, and the difficulty of performing parameter inference and optimisation tasks. This in turn has sparked interest in the construction of differentiable ABMs as a strategy for combatting these difficulties, yet a number of challenges remain. In this paper, we discuss and present experiments that highlight some of these challenges, along with potential solutions.

Alessandro Abate, Yousif Almulla, James Fox et al.

Training reinforcement learning (RL) agents using scalar reward signals is often infeasible when an environment has sparse and non-Markovian rewards. Moreover, handcrafting these reward functions before training is prone to misspecification, especially when the environment's dynamics are only partially known. This paper proposes a novel pipeline for learning non-Markovian task specifications as succinct finite-state `task automata' from episodes of agent experience within unknown environments. We leverage two key algorithmic insights. First, we learn a product MDP, a model composed of the specification's automaton and the environment's MDP (both initially unknown), by treating the product MDP as a partially observable MDP and using the well-known Baum-Welch algorithm for learning hidden Markov models. Second, we propose a novel method for distilling the task automaton (assumed to be a deterministic finite automaton) from the learnt product MDP. Our learnt task automaton enables the decomposition of a task into its constituent sub-tasks, which improves the rate at which an RL agent can later synthesise an optimal policy. It also provides an interpretable encoding of high-level environmental and task features, so a human can readily verify that the agent has learnt coherent tasks with no misspecifications. In addition, we take steps towards ensuring that the learnt automaton is environment-agnostic, making it well-suited for use in transfer learning. Finally, we provide experimental results compared with two baselines to illustrate our algorithm's performance in different environments and tasks.

James Fox, Matt MacDermott, Lewis Hammond et al.

Multi-agent influence diagrams (MAIDs) are a popular game-theoretic model based on Bayesian networks. In some settings, MAIDs offer significant advantages over extensive-form game representations. Previous work on MAIDs has assumed that agents employ behavioural policies, which set independent conditional probability distributions over actions for each of their decisions. In settings with imperfect recall, however, a Nash equilibrium in behavioural policies may not exist. We overcome this by showing how to solve MAIDs with forgetful and absent-minded agents using mixed policies and two types of correlated equilibrium. We also analyse the computational complexity of key decision problems in MAIDs, and explore tractable cases. Finally, we describe applications of MAIDs to Markov games and team situations, where imperfect recall is often unavoidable.

Emanuele La Malfa, Ping Zhu, Samuele Marro et al.

We present an end-to-end framework for planning supported by verifiers. An orchestrator receives a human specification written in natural language and converts it into a PDDL (Planning Domain Definition Language) model, where the domain and problem are iteratively refined by sub-modules (agents) to address common planning requirements, such as time constraints and optimality, as well as ambiguities and contradictions that may exist in the human specification. The validated domain and problem are then passed to an external planning engine to generate a plan. The orchestrator and agents are powered by Large Language Models (LLMs) and require no human intervention at any stage of the process. Finally, a module translates the final plan back into natural language to improve human readability while maintaining the correctness of each step. We demonstrate the flexibility and effectiveness of our framework across various domains and tasks, including the Google NaturalPlan benchmark and PlanBench, as well as planning problems like Blocksworld and the Tower of Hanoi (where LLMs are known to struggle even with small instances). Our framework can be integrated with any PDDL planning engine and validator (such as Fast Downward, LPG, POPF, VAL, and uVAL, which we have tested) and represents a significant step toward end-to-end planning aided by LLMs.

Imran Mahmood, Nicholas Bishop, Anisoara Calinescu et al.

In agent-based simulations, synthetic populations of agents are commonly used to represent the structure, behaviour, and interactions of individuals. However, generating a synthetic population that accurately reflects real population statistics is a challenging task, particularly when performed at scale. In this paper, we propose a multi objective combinatorial optimisation technique for large scale population synthesis. We demonstrate the effectiveness of our approach by generating a synthetic population for selected regions and validating it on contingency tables from real population data. Our approach supports complex hierarchical structures between individuals and households, is scalable to large populations and achieves minimal contigency table reconstruction error. Hence, it provides a useful tool for policymakers and researchers for simulating the dynamics of complex populations.

M Lopes Alves, Joel Dyer, Doyne Farmer et al.

Agent-based modelling (ABM) is a widespread approach to simulate complex systems. Advancements in computational processing and storage have facilitated the adoption of ABMs across many fields; however, ABMs face challenges that limit their use as decision-support tools. A significant issue is parameter estimation in large-scale ABMs, particularly due to computational constraints on exploring the parameter space. This study evaluates a state-of-the-art simulation-based inference (SBI) framework that uses neural networks (NN) for parameter estimation. This framework is applied to an established labour market ABM based on job transition networks. The ABM is initiated with synthetic datasets and the real U.S. labour market. Next, we compare the effectiveness of summary statistics derived from a list of statistical measures with that learned by an embedded NN. The results demonstrate that the NN-based approach recovers the original parameters when evaluating posterior distributions across various dataset scales and improves efficiency compared to traditional Bayesian methods.

Lewis Hammond, James Fox, Tom Everitt et al.

Multi-agent influence diagrams (MAIDs) are a popular form of graphical model that, for certain classes of games, have been shown to offer key complexity and explainability advantages over traditional extensive form game (EFG) representations. In this paper, we extend previous work on MAIDs by introducing the concept of a MAID subgame, as well as subgame perfect and trembling hand perfect equilibrium refinements. We then prove several equivalence results between MAIDs and EFGs. Finally, we describe an open source implementation for reasoning about MAIDs and computing their equilibria.

Gabriele La Malfa, Emanuele La Malfa, Saar Cohen et al.

Self-play red team is an established approach to improving AI safety in which different instances of the same model play attacker and defender roles in a zero-sum game, i.e., where the attacker tries to jailbreak the defender; if self-play converges to a Nash equilibrium, the model is guaranteed to respond safely within the settings of the game. Although the parameter sharing enforced by the use of the same model for the two roles improves stability and performance, it introduces fundamental theoretical and architectural limitations. We show that the set of Nash equilibria that can be reached corresponds to a broad class of behaviours that includes trivial always refuse strategies and oracle-like defenders, thus limiting practical applicability. We then show that when attacker and defender share and update the same base model, the dynamics collapse to self-consistency, so that attacks do not enforce adversarial pressure on the defender. In response, we propose Anchored Bipolicy Self-Play, which trains distinct role-specific LoRA adapters on top of a frozen base model, thereby maintaining stable optimisation while preserving adversarial pressure through explicit role separation. In relation to standard self-play, we show up to 100x greater parameter efficiency than finetuning and consistent improvements in safety compared to self-play fine-tuned models. We evaluate on Qwen2.5-{3B, 7B,14B}-IT models across widely used safety benchmarks, showing improved robustness without loss of reasoning ability. Cross-play experiments further show that our attacker and defender models are superior to self-play in terms of adversarial defence and safety.

Samuele Marro, Emanuele La Malfa, Jesse Wright et al. · oxford

Communication is a prerequisite for collaboration. When scaling networks of AI-powered agents, communication must be versatile, efficient, and portable. These requisites, which we refer to as the Agent Communication Trilemma, are hard to achieve in large networks of agents. We introduce Agora, a meta protocol that leverages existing communication standards to make LLM-powered agents solve complex problems efficiently. In Agora, agents typically use standardised routines for frequent communications, natural language for rare communications, and LLM-written routines for everything in between. Agora sidesteps the Agent Communication Trilemma and robustly handles changes in interfaces and members, allowing unprecedented scalability with full decentralisation and minimal involvement of human beings. On large Agora networks, we observe the emergence of self-organising, fully automated protocols that achieve complex goals without human intervention.

Emanuele La Malfa, Christoph Weinhuber, Orazio Torre et al. · oxford

Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. This work studies to what extent Large Language Models (LLMs) can simulate coding and algorithmic tasks to provide insights into general capabilities in such algorithmic reasoning tasks. We introduce benchmarks for straight-line programs, code that contains critical paths, and approximate and redundant instructions. We further assess the simulation capabilities of LLMs with sorting algorithms and nested loops and show that a routine's computational complexity directly affects an LLM's ability to simulate its execution. While the most powerful LLMs exhibit relatively strong simulation capabilities, the process is fragile, seems to rely heavily on pattern recognition, and is affected by memorisation. We propose a novel off-the-shelf prompting method, Chain of Simulation (CoSm), which instructs LLMs to simulate code execution line by line/follow the computation pattern of compilers. CoSm efficiently helps LLMs reduce memorisation and shallow pattern recognition while improving simulation performance. We consider the success of CoSm in code simulation to be inspirational for other general routine simulation reasoning tasks.

Joel Dyer, Nicholas Bishop, Yorgos Felekis et al.

Agent-based simulators provide granular representations of complex intelligent systems by directly modelling the interactions of the system's constituent agents. Their high-fidelity nature enables hyper-local policy evaluation and testing of what-if scenarios, but is associated with large computational costs that inhibits their widespread use. Surrogate models can address these computational limitations, but they must behave consistently with the agent-based model under policy interventions of interest. In this paper, we capitalise on recent developments on causal abstractions to develop a framework for learning interventionally consistent surrogate models for agent-based simulators. Our proposed approach facilitates rapid experimentation with policy interventions in complex systems, while inducing surrogates to behave consistently with high probability with respect to the agent-based simulator across interventions of interest. We demonstrate with empirical studies that observationally trained surrogates can misjudge the effect of interventions and misguide policymakers towards suboptimal policies, while surrogates trained for interventional consistency with our proposed method closely mimic the behaviour of an agent-based model under interventions of interest.

Fabio Massimo Zennaro, Nicholas Bishop, Joel Dyer et al.

Multi-armed bandits (MAB) and causal MABs (CMAB) are established frameworks for decision-making problems. The majority of prior work typically studies and solves individual MAB and CMAB in isolation for a given problem and associated data. However, decision-makers are often faced with multiple related problems and multi-scale observations where joint formulations are needed in order to efficiently exploit the problem structures and data dependencies. Transfer learning for CMABs addresses the situation where models are defined on identical variables, although causal connections may differ. In this work, we extend transfer learning to setups involving CMABs defined on potentially different variables, with varying degrees of granularity, and related via an abstraction map. Formally, we introduce the problem of causally abstracted MABs (CAMABs) by relying on the theory of causal abstraction in order to express a rigorous abstraction map. We propose algorithms to learn in a CAMAB, and study their regret. We illustrate the limitations and the strengths of our algorithms on a real-world scenario related to online advertising.

Emanuele La Malfa, Gabriele La Malfa, Samuele Marro et al. · oxford

Recent interest in Multi-Agent Systems of Large Language Models (MAS LLMs) has led to an increase in frameworks leveraging multiple LLMs to tackle complex tasks. However, much of this literature appropriates the terminology of MAS without engaging with its foundational principles. In this position paper, we highlight critical discrepancies between MAS theory and current MAS LLMs implementations, focusing on four key areas: the social aspect of agency, environment design, coordination and communication protocols, and measuring emergent behaviours. Our position is that many MAS LLMs lack multi-agent characteristics such as autonomy, social interaction, and structured environments, and often rely on oversimplified, LLM-centric architectures. The field may slow down and lose traction by revisiting problems the MAS literature has already addressed. Therefore, we systematically analyse this issue and outline associated research opportunities; we advocate for better integrating established MAS concepts and more precise terminology to avoid mischaracterisation and missed opportunities.

Fangru Lin, Shaoguang Mao, Emanuele La Malfa et al. · oxford

Language is not monolithic. While benchmarks, including those designed for multiple languages, are often used as proxies to evaluate the performance of Large Language Models (LLMs), they tend to overlook the nuances of within-language variation and thus fail to model the experience of speakers of non-standard dialects. Focusing on African American Vernacular English (AAVE), we present the first study aimed at objectively assessing the fairness and robustness of LLMs in handling dialects across canonical reasoning tasks, including algorithm, math, logic, and integrated reasoning. We introduce ReDial (Reasoning with Dialect Queries), a benchmark containing 1.2K+ parallel query pairs in Standardized English and AAVE. We hire AAVE speakers, including experts with computer science backgrounds, to rewrite seven popular benchmarks, such as HumanEval and GSM8K. With ReDial, we evaluate widely used LLMs, including GPT, Claude, Llama, Mistral, and the Phi model families. Our findings reveal that almost all of these widely used models show significant brittleness and unfairness to queries in AAVE. Our work establishes a systematic and objective framework for analyzing LLM bias in dialectal queries. Moreover, it highlights how mainstream LLMs provide unfair service to dialect speakers in reasoning tasks, laying a critical foundation for future research.

Samuele Marro, Davide Evangelista, X. Angelo Huang et al. · oxford

Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based language models implicitly learn to represent sentences as continuous-time functions defined over a continuous input space. This phenomenon occurs in most state-of-the-art Large Language Models (LLMs), including Llama2, Llama3, Phi3, Gemma, Gemma2, and Mistral, and suggests that LLMs reason about language in ways that fundamentally differ from humans. Our work formally extends Transformers to capture the nuances of time and space continuity in both input and output space. Our results challenge the traditional interpretation of how LLMs understand language, with several linguistic and engineering implications.

Arnau Quera-Bofarull, Nicholas Bishop, Joel Dyer et al.

Agent-based models (ABMs) simulate complex systems by capturing the bottom-up interactions of individual agents comprising the system. Many complex systems of interest, such as epidemics or financial markets, involve thousands or even millions of agents. Consequently, ABMs often become computationally demanding and rely on the calibration of numerous free parameters, which has significantly hindered their widespread adoption. In this paper, we demonstrate that automatic differentiation (AD) techniques can effectively alleviate these computational burdens. By applying AD to ABMs, the gradients of the simulator become readily available, greatly facilitating essential tasks such as calibration and sensitivity analysis. Specifically, we show how AD enables variational inference (VI) techniques for efficient parameter calibration. Our experiments demonstrate substantial performance improvements and computational savings using VI on three prominent ABMs: Axtell's model of firms; Sugarscape; and the SIR epidemiological model. Our approach thus significantly enhances the practicality and scalability of ABMs for studying complex systems.

Daniel Jarne Ornia, Nicholas Bishop, Joel Dyer et al.

Advanced reasoning models with agentic capabilities (AI agents) are deployed to interact with humans and to solve sequential decision-making problems under (approximate) utility functions and internal models. When such problems have resource or failure constraints where action sequences may be forcibly terminated once resources are exhausted, agents face implicit trade-offs that reshape their utility-driven (rational) behaviour. Additionally, since these agents are typically commissioned by a human principal to act on their behalf, asymmetries in constraint exposure can give rise to previously unanticipated misalignment between human objectives and agent incentives. We formalise this setting through a survival bandit framework, provide theoretical and empirical results that quantify the impact of survival-driven preference shifts, identify conditions under which misalignment emerges and propose mechanisms to mitigate the emergence of risk-seeking or risk-averse behaviours. As a result, this work aims to increase understanding and interpretability of emergent behaviours of AI agents operating under such survival pressure, and offer guidelines for safely deploying such AI systems in critical resource-limited environments.

Emanuele La Malfa, Christoph Weinhuber, Orazio Torre et al. · oxford

Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. We collect pairs of naturalistic and synthetic reasoning tasks to assess the capabilities of Large Language Models (LLM). While naturalistic tasks often require careful human handcrafting, we show that synthetic data is, in many cases, a good proxy that is much easier to collect at scale. We leverage common constructs in programming as the counterpart of the building blocks of naturalistic reasoning tasks, such as straight-line programs, code that contains critical paths, and approximate and redundant instructions. We further assess the capabilities of LLMs on sorting problems and repeated operations via sorting algorithms and nested loops. Our synthetic datasets further reveal that while the most powerful LLMs exhibit relatively strong execution capabilities, the process is fragile: it is negatively affected by memorisation and seems to rely heavily on pattern recognition. Our contribution builds upon synthetically testing the reasoning capabilities of LLMs as a scalable complement to handcrafted human-annotated problems.

Oliver Goldstein, Emanuele La Malfa, Felix Drinkall et al. · oxford

We discuss the ``Infinitely Many Paraphrases'' attacks (IMP), a category of jailbreaks that leverages the increasing capabilities of a model to handle paraphrases and encoded communications to bypass their defensive mechanisms. IMPs' viability pairs and grows with a model's capabilities to handle and bind the semantics of simple mappings between tokens and work extremely well in practice, posing a concrete threat to the users of the most powerful LLMs in commerce. We show how one can bypass the safeguards of the most powerful open- and closed-source LLMs and generate content that explicitly violates their safety policies. One can protect against IMPs by improving the guardrails and making them scale with the LLMs' capabilities. For two categories of attacks that are straightforward to implement, i.e., bijection and encoding, we discuss two defensive strategies, one in token and the other in embedding space. We conclude with some research questions we believe should be prioritised to enhance the defensive mechanisms of LLMs and our understanding of their safety.

Samuele Marro, Jialin Yu, Emanuele La Malfa et al.

As frontier Large Language Models (LLMs) increasingly saturate new benchmarks shortly after they are published, benchmarking itself is at a juncture: if frontier models keep improving, it will become increasingly hard for humans to generate discriminative tasks, provide accurate ground-truth answers, or evaluate complex solutions. If benchmarking becomes infeasible, our ability to measure any progress in AI is at stake. We refer to this scenario as the post-comprehension regime. In this work, we propose Critique-Resilient Benchmarking, an adversarial framework designed to compare models even when full human understanding is infeasible. Our technique relies on the notion of critique-resilient correctness: an answer is deemed correct if no adversary has convincingly proved otherwise. Unlike standard benchmarking, humans serve as bounded verifiers and focus on localized claims, which preserves evaluation integrity beyond full comprehension of the task. Using an itemized bipartite Bradley-Terry model, we jointly rank LLMs by their ability to solve challenging tasks and to generate difficult yet solvable questions. We showcase the effectiveness of our method in the mathematical domain across eight frontier LLMs, showing that the resulting scores are stable and correlate with external capability measures. Our framework reformulates benchmarking as an adversarial generation-evaluation game in which humans serve as final adjudicators.

Daniel Jarne Ornia, Joel Dyer, Nicholas Bishop et al.

Complex learning agents are increasingly deployed alongside existing experts, such as human operators or previously trained agents. However, it remains unclear how should learners optimally incorporate certain forms of expert data, which may differ in structure from the learner's own action-outcome experiences. We study this problem in the context of Bayesian multi-armed bandits, considering: (i) offline settings, where the learner receives a dataset of outcomes from the expert's optimal policy before interaction, and (ii) simultaneous settings, where the learner must choose at each step whether to update its beliefs based on its own experience, or based on the outcome simultaneously achieved by an expert. We formalize how expert data influences the learner's posterior, and prove that pretraining on expert outcomes tightens information-theoretic regret bounds by the mutual information between the expert data and the optimal action. For the simultaneous setting, we propose an information-directed rule where the learner processes the data source that maximizes their one-step information gain about the optimal action. Finally, we propose strategies for how the learner can infer when to trust the expert and when not to, safeguarding the learner for the cases where the expert is ineffective or compromised. By quantifying the value of expert data, our framework provides practical, information-theoretic algorithms for agents to intelligently decide when to learn from others.

Joel Dyer, Daniel Jarne Ornia, Nicholas Bishop et al.

Evaluating the safety of frontier AI systems is an increasingly important concern, helping to measure the capabilities of such models and identify risks before deployment. However, it has been recognised that if AI agents are aware that they are being evaluated, such agents may deliberately hide dangerous capabilities or intentionally demonstrate suboptimal performance in safety-related tasks in order to be released and to avoid being deactivated or retrained. Such strategic deception - often known as "sandbagging" - threatens to undermine the integrity of safety evaluations. For this reason, it is of value to identify methods that enable us to distinguish behavioural patterns that demonstrate a true lack of capability from behavioural patterns that are consistent with sandbagging. In this paper, we develop a simple model of strategic deception in sequential decision-making tasks, inspired by the recently developed survival bandit framework. We demonstrate theoretically that this problem induces sandbagging behaviour in optimal rational agents, and construct a statistical test to distinguish between sandbagging and incompetence from sequences of test scores. In simulation experiments, we investigate the reliability of this test in allowing us to distinguish between such behaviours in bandit models. This work aims to establish a potential avenue for developing robust statistical procedures for use in the science of frontier model evaluations.

Joel Dyer, Nicholas Bishop, Anisoara Calinescu et al.

Although real-world decision-making problems can often be encoded as causal multi-armed bandits (CMABs) at different levels of abstraction, a general methodology exploiting the information and computational advantages of each abstraction level is missing. In this paper, we propose AT-UCB, an algorithm which efficiently exploits shared information between CMAB problem instances defined at different levels of abstraction. More specifically, AT-UCB leverages causal abstraction (CA) theory to explore within a cheap-to-simulate and coarse-grained CMAB instance, before employing the traditional upper confidence bound (UCB) algorithm on a restricted set of potentially optimal actions in the CMAB of interest, leading to significant reductions in cumulative regret when compared to the classical UCB algorithm. We illustrate the advantages of AT-UCB theoretically, through a novel upper bound on the cumulative regret, and empirically, by applying AT-UCB to epidemiological simulators with varying resolution and computational cost.

Emanuele La Malfa, Jon Vadillo, Marco Molinari et al. · oxford

This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point explanations satisfy properties like minimality, stability, and faithfulness, revealing hidden model behaviours and explanatory weaknesses. We define convergence conditions for several classes of explainers, from feature-based to mechanistic tools like Sparse AutoEncoders, and we report quantitative and qualitative results for several datasets and models, including LLMs such as Llama-3.3-70B.

Jonathan Shaki, Emanuele La Malfa, Michael Wooldridge et al. · oxford

We study how large language models (LLMs) reason about memorized knowledge through simple binary relations such as equality ($=$), inequality ($<$), and inclusion ($\subset$). Unlike in-context reasoning, the axioms (e.g., $a < b, b < c$) are only seen during training and not provided in the task prompt (e.g., evaluating $a < c$). The tasks require one or more reasoning steps, and data aggregation from one or more sources, showing performance change with task complexity. We introduce a lightweight technique, out-of-context representation learning, which trains only new token embeddings on axioms and evaluates them on unseen tasks. Across reflexivity, symmetry, and transitivity tests, LLMs mostly perform statistically significant better than chance, making the correct answer extractable when testing multiple phrasing variations, but still fall short of consistent reasoning on every single query. Analysis shows that the learned embeddings are organized in structured ways, suggesting real relational understanding. Surprisingly, it also indicates that the core reasoning happens during the training, not inference.

X. Angelo Huang, Emanuele La Malfa, Samuele Marro et al.

Theory of Mind (ToM) can be used to assess the capabilities of Large Language Models (LLMs) in complex scenarios where social reasoning is required. While the research community has proposed many ToM benchmarks, their hardness varies greatly, and their complexity is not well defined. This work proposes a framework inspired by cognitive load theory to measure the complexity of ToM tasks. We quantify a problem's complexity as the number of states necessary to solve it correctly. Our complexity measure also accounts for spurious states of a ToM problem designed to make it apparently harder. We use our method to assess the complexity of five widely adopted ToM benchmarks. On top of this framework, we design a prompting technique that augments the information available to a model with a description of how the environment changes with the agents' interactions. We name this technique Discrete World Models (DWM) and show how it elicits superior performance on ToM tasks.

Manuj Mishra, James Fox, Michael Wooldridge

Causal games are probabilistic graphical models that enable causal queries to be answered in multi-agent settings. They extend causal Bayesian networks by specifying decision and utility variables to represent the agents' degrees of freedom and objectives. In multi-agent settings, whether each agent decides on their policy before or after knowing the causal intervention is important as this affects whether they can respond to the intervention by adapting their policy. Consequently, previous work in causal games imposed chronological constraints on permissible interventions. We relax this by outlining a sound and complete set of primitive causal interventions so the effect of any arbitrarily complex interventional query can be studied in multi-agent settings. We also demonstrate applications to the design of safe AI systems by considering causal mechanism design and commitment.

Arnau Quera-Bofarull, Ayush Chopra, Anisoara Calinescu et al.

Agent-based modelling (ABMing) is a powerful and intuitive approach to modelling complex systems; however, the intractability of ABMs' likelihood functions and the non-differentiability of the mathematical operations comprising these models present a challenge to their use in the real world. These difficulties have in turn generated research on approximate Bayesian inference methods for ABMs and on constructing differentiable approximations to arbitrary ABMs, but little work has been directed towards designing approximate Bayesian inference techniques for the specific case of differentiable ABMs. In this work, we aim to address this gap and discuss how generalised variational inference procedures may be employed to provide misspecification-robust Bayesian parameter inferences for differentiable ABMs. We demonstrate with experiments on a differentiable ABM of the COVID-19 pandemic that our approach can result in accurate inferences, and discuss avenues for future work.

Dongge Han, Chris Xiaoxuan Lu, Tomasz Michalak et al.

Deep reinforcement learning (RL) has recently shown great promise in robotic continuous control tasks. Nevertheless, prior research in this vein center around the centralized learning setting that largely relies on the communication availability among all the components of a robot. However, agents in the real world often operate in a decentralised fashion without communication due to latency requirements, limited power budgets and safety concerns. By formulating robotic components as a system of decentralised agents, this work presents a decentralised multiagent reinforcement learning framework for continuous control. To this end, we first develop a cooperative multiagent PPO framework that allows for centralized optimisation during training and decentralised operation during execution. However, the system only receives a global reward signal which is not attributed towards each agent. To address this challenge, we further propose a generic game-theoretic credit assignment framework which computes agent-specific reward signals. Last but not least, we also incorporate a model-based RL module into our credit assignment framework, which leads to significant improvement in sample efficiency. We demonstrate the effectiveness of our framework on experimental results on Mujoco locomotion control tasks. For a demo video please visit: https://youtu.be/gFyVPm4svEY.

Julian Gutierrez, Lewis Hammond, Anthony W. Lin et al.

Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a game-theoretic equilibrium. Previous work in this area has largely focussed on deterministic systems. In this paper, we develop the theory and algorithms for rational verification in probabilistic systems. We focus on concurrent stochastic games (CSGs), which can be used to model uncertainty and randomness in complex multi-agent environments. We study the rational verification problem for both non-cooperative games and cooperative games in the qualitative probabilistic setting. In the former case, we consider LTL properties satisfied by the Nash equilibria of the game and in the latter case LTL properties satisfied by the core. In both cases, we show that the problem is 2EXPTIME-complete, thus not harder than the much simpler verification problem of model checking LTL properties of systems modelled as Markov decision processes (MDPs).

Julian Gutierrez, Muhammad Najib, Giuseppe Perelli et al.

In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance, an equilibrium satisfying a given temporal logic property -- a problem that we call equilibrium design. We base our study on a framework where system specifications are represented as temporal logic formulae, games as quantitative concurrent game structures, and players' goals as mean-payoff objectives. In particular, we consider system specifications given by LTL and GR(1) formulae, and show that implementing a mechanism to ensure that a given temporal logic property is satisfied on some/every Nash equilibrium of the game, whenever such a mechanism exists, can be done in PSPACE for LTL properties and in NP/$Σ^{P}_{2}$ for GR(1) specifications. We also study the complexity of various related decision and optimisation problems, such as optimality and uniqueness of solutions, and show that the complexities of all such problems lie within the polynomial hierarchy. As an application, equilibrium design can be used as an alternative solution to the rational synthesis and verification problems for concurrent games with mean-payoff objectives whenever no solution exists, or as a technique to repair, whenever possible, concurrent games with undesirable rational outcomes (Nash equilibria) in an optimal way.

Lewis Hammond, Alessandro Abate, Julian Gutierrez et al.

In this paper, we study the problem of learning to satisfy temporal logic specifications with a group of agents in an unknown environment, which may exhibit probabilistic behaviour. From a learning perspective these specifications provide a rich formal language with which to capture tasks or objectives, while from a logic and automated verification perspective the introduction of learning capabilities allows for practical applications in large, stochastic, unknown environments. The existing work in this area is, however, limited. Of the frameworks that consider full linear temporal logic or have correctness guarantees, all methods thus far consider only the case of a single temporal logic specification and a single agent. In order to overcome this limitation, we develop the first multi-agent reinforcement learning technique for temporal logic specifications, which is also novel in its ability to handle multiple specifications. We provide correctness and convergence guarantees for our main algorithm - ALMANAC (Automaton/Logic Multi-Agent Natural Actor-Critic) - even when using function approximation. Alongside our theoretical results, we further demonstrate the applicability of our technique via a set of preliminary experiments.

Julian Gutierrez, Giuseppe Perelli, Michael Wooldridge

Linear Dynamic Logic on finite traces LDLf is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLf. This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because LDLf goals are considered, in the settings we study -- Reactive Modules games and iterated Boolean games with goals over finite traces -- players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with LDLf objectives is regular, and provides complexity results for the associated automata constructions.

Julian Gutierrez, Aniello Murano, Giuseppe Perelli et al.

The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act independently and strategically in pursuit of personal preferences. In this article, we study these games in the context of finite-memory strategies, and we assume players' preferences are defined by a qualitative and a quantitative objective, which are related by a lexicographic order: a player first prefers to satisfy its qualitative objective (given as a formula of Linear Temporal Logic) and then prefers to minimise costs (given by a mean-payoff function). Our main result is that deciding the existence of a strict epsilon Nash equilibrium in such games is 2ExpTime-complete (and hence decidable), even if players' deviations are implemented as infinite-memory strategies.

Julian Gutierrez, Muhammad Najib, Giuseppe Perelli et al.

In the context of multi-agent systems, the rational verification problem is concerned with checking which temporal logic properties will hold in a system when its constituent agents are assumed to behave rationally and strategically in pursuit of individual objectives. Typically, those objectives are expressed as temporal logic formulae which the relevant agent desires to see satisfied. Unfortunately, rational verification is computationally complex, and requires specialised techniques in order to obtain practically useable implementations. In this paper, we present such a technique. This technique relies on a reduction of the rational verification problem to the solution of a collection of parity games. Our approach has been implemented in the Equilibrium Verification Environment (EVE) system. The EVE system takes as input a model of a concurrent/multi-agent system represented using the Simple Reactive Modules Language (SRML), where agent goals are represented as Linear Temporal Logic (LTL) formulae, together with a claim about the equilibrium behaviour of the system, also expressed as an LTL formula. EVE can then check whether the LTL claim holds on some (or every) computation of the system that could arise through agents choosing Nash equilibrium strategies; it can also check whether a system has a Nash equilibrium, and synthesise individual strategies for players in the multi-player game. After presenting our basic framework, we describe our new technique and prove its correctness. We then describe our implementation in the EVE system, and present experimental results which show that EVE performs favourably in comparison to other existing tools that support rational verification.

Dongge Han, Michael Wooldridge, Alex Rogers et al.

Submodular functions have been a powerful mathematical model for a wide range of real-world applications. Recently, submodular functions are becoming increasingly important in machine learning (ML) for modelling notions such as information and redundancy among entities such as data and features. Among these applications, a key question is payoff allocation, i.e., how to evaluate the importance of each entity towards the collective objective? To this end, classic solution concepts from cooperative game theory offer principled approaches to payoff allocation. However, despite the extensive body of game-theoretic literature, payoff allocation in submodular games are relatively under-researched. In particular, an important notion that arises in the emerging submodular applications is redundancy, which may occur from various sources such as abundant data or malicious manipulations where a player replicates its resource and act under multiple identities. Though many game-theoretic solution concepts can be directly used in submodular games, naively applying them for payoff allocation in these settings may incur robustness issues against replication. In this paper, we systematically study the replication manipulation in submodular games and investigate replication robustness, a metric that quantitatively measures the robustness of solution concepts against replication. Using this metric, we present conditions which theoretically characterise the robustness of semivalues, a wide family of solution concepts including the Shapley and Banzhaf value. Moreover, we empirically validate our theoretical results on an emerging submodular ML application, i.e., the ML data market.

Dongge Han, Wendelin Boehmer, Michael Wooldridge et al.

In a multi-agent system, an agent's optimal policy will typically depend on the policies chosen by others. Therefore, a key issue in multi-agent systems research is that of predicting the behaviours of others, and responding promptly to changes in such behaviours. One obvious possibility is for each agent to broadcast their current intention, for example, the currently executed option in a hierarchical reinforcement learning framework. However, this approach results in inflexibility of agents if options have an extended duration and are dynamic. While adjusting the executed option at each step improves flexibility from a single-agent perspective, frequent changes in options can induce inconsistency between an agent's actual behaviour and its broadcast intention. In order to balance flexibility and predictability, we propose a dynamic termination Bellman equation that allows the agents to flexibly terminate their options. We evaluate our model empirically on a set of multi-agent pursuit and taxi tasks, and show that our agents learn to adapt flexibly across scenarios that require different termination behaviours.

Jiarui Gan, Qingyu Guo, Long Tran-Thanh et al.

In Stackelberg security games when information about the attacker's payoffs is uncertain, algorithms have been proposed to learn the optimal defender commitment by interacting with the attacker and observing their best responses. In this paper, we show that, however, these algorithms can be easily manipulated if the attacker responds untruthfully. As a key finding, attacker manipulation normally leads to the defender learning a maximin strategy, which effectively renders the learning attempt meaningless as to compute a maximin strategy requires no additional information about the other player at all. We then apply a game-theoretic framework at a higher level to counteract such manipulation, in which the defender commits to a policy that specifies her strategy commitment according to the learned information. We provide a polynomial-time algorithm to compute the optimal such policy, and in addition, a heuristic approach that applies even when the attacker's payoff space is infinite or completely unknown. Empirical evaluation shows that our approaches can improve the defender's utility significantly as compared to the situation when attacker manipulation is ignored.

Mateusz K. Tarkowski, Tomasz P. Michalak, Talal Rahwan et al.

Game-theoretic centrality is a flexible and sophisticated approach to identify the most important nodes in a network. It builds upon the methods from cooperative game theory and network theory. The key idea is to treat nodes as players in a cooperative game, where the value of each coalition is determined by certain graph-theoretic properties. Using solution concepts from cooperative game theory, it is then possible to measure how responsible each node is for the worth of the network. The literature on the topic is already quite large, and is scattered among game-theoretic and computer science venues. We review the main game-theoretic network centrality measures from both bodies of literature and organize them into two categories: those that are more focused on the connectivity of nodes, and those that are more focused on the synergies achieved by nodes in groups. We present and explain each centrality, with a focus on algorithms and complexity.

Haris Aziz, Paul Harrenstein, Jérôme Lang et al.

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.

Wiebe van der Hoek, Dirk Walther, Michael Wooldridge

We present DCL-PC: a logic for reasoning about how the abilities of agents and coalitions of agents are altered by transferring control from one agent to another. The logical foundation of DCL-PC is CL-PC, a logic for reasoning about cooperation in which the abilities of agents and coalitions of agents stem from a distribution of atomic Boolean variables to individual agents -- the choices available to a coalition correspond to assignments to the variables the coalition controls. The basic modal constructs of DCL-PC are of the form coalition C can cooperate to bring about phi. DCL-PC extends CL-PC with dynamic logic modalities in which atomic programs are of the form agent i gives control of variable p to agent j; as usual in dynamic logic, these atomic programs may be combined using sequence, iteration, choice, and test operators to form complex programs. By combining such dynamic transfer programs with cooperation modalities, it becomes possible to reason about how the power of agents and coalitions is affected by the transfer of control. We give two alternative semantics for the logic: a direct semantics, in which we capture the distributions of Boolean variables to agents; and a more conventional Kripke semantics. We prove that these semantics are equivalent, and then present an axiomatization for the logic. We investigate the computational complexity of model checking and satisfiability for DCL-PC, and show that both problems are PSPACE-complete (and hence no worse than the underlying logic CL-PC). Finally, we investigate the characterisation of control in DCL-PC. We distinguish between first-order control -- the ability of an agent or coalition to control some state of affairs through the assignment of values to the variables under the control of the agent or coalition -- and second-order control -- the ability of an agent to exert control over the control that other agents have by transferring variables to other agents. We give a logical characterisation of second-order control.