Mirco Musolesi

James Rudd-Jones, María Pérez-Ortiz, Mirco Musolesi

Analysing learning in Multi-Agent Reinforcement Learning (MARL) environments is challenging, in particular with respect to \textit{individual} decision-making. Practitioners frequently struggle to compare training runs due to the inherent stochasticity in algorithms arising from random dithering exploration, environment transition noise, and stochastic gradient updates to name a few. Traditional analytical approaches, such as replicator dynamics, oft rely on mean-field approximations to remove stochastic effects, but this simplification, whilst able to provide general overall trends, can lead to dissonance between analytical predictions and actual agent realisations. We propose modelling MARL training as a \textit{coupled stochastic dynamical systems}, capturing both agent interactions and environmental characteristics. Leveraging tools from dynamical systems theory, we pragmatically analyse the stability and sensitivity of agent behaviour, which are key dimensions for their practical deployments, for example, in presence of strict safety requirements. This framework allows us to rigorously study the inherent stochasticity of MARL, providing a deeper understanding of system behaviour.

Giorgio Franceschelli, Mirco Musolesi

Large Language Models (LLMs) are revolutionizing several areas of Artificial Intelligence. One of the most remarkable applications is creative writing, e.g., poetry or storytelling: the generated outputs are often of astonishing quality. However, a natural question arises: can LLMs be really considered creative? In this article, we first analyze the development of LLMs under the lens of creativity theories, investigating the key open questions and challenges. In particular, we focus our discussion on the dimensions of value, novelty, and surprise as proposed by Margaret Boden in her work. Then, we consider different classic perspectives, namely product, process, press, and person. We discuss a set of ``easy'' and ``hard'' problems in machine creativity, presenting them in relation to LLMs. Finally, we examine the societal impact of these technologies with a particular focus on the creative industries, analyzing the opportunities offered, the challenges arising from them, and the potential associated risks, from both legal and ethical points of view.

Giorgio Franceschelli, Mirco Musolesi

Generative Artificial Intelligence (AI) is one of the most exciting developments in Computer Science of the last decade. At the same time, Reinforcement Learning (RL) has emerged as a very successful paradigm for a variety of machine learning tasks. In this survey, we discuss the state of the art, opportunities and open research questions in applying RL to generative AI. In particular, we will discuss three types of applications, namely, RL as an alternative way for generation without specified objectives; as a way for generating outputs while concurrently maximizing an objective function; and, finally, as a way of embedding desired characteristics, which cannot be easily captured by means of an objective function, into the generative process. We conclude the survey with an in-depth discussion of the opportunities and challenges in this fascinating emerging area.

Elizaveta Tennant, Stephen Hailes, Mirco Musolesi

Practical uses of Artificial Intelligence (AI) in the real world have demonstrated the importance of embedding moral choices into intelligent agents. They have also highlighted that defining top-down ethical constraints on AI according to any one type of morality is extremely challenging and can pose risks. A bottom-up learning approach may be more appropriate for studying and developing ethical behavior in AI agents. In particular, we believe that an interesting and insightful starting point is the analysis of emergent behavior of Reinforcement Learning (RL) agents that act according to a predefined set of moral rewards in social dilemmas. In this work, we present a systematic analysis of the choices made by intrinsically-motivated RL agents whose rewards are based on moral theories. We aim to design reward structures that are simplified yet representative of a set of key ethical systems. Therefore, we first define moral reward functions that distinguish between consequence- and norm-based agents, between morality based on societal norms or internal virtues, and between single- and mixed-virtue (e.g., multi-objective) methodologies. Then, we evaluate our approach by modeling repeated dyadic interactions between learning moral agents in three iterated social dilemma games (Prisoner's Dilemma, Volunteer's Dilemma and Stag Hunt). We analyze the impact of different types of morality on the emergence of cooperation, defection or exploitation, and the corresponding social outcomes. Finally, we discuss the implications of these findings for the development of moral agents in artificial and mixed human-AI societies.

Ho Long Fung, Victor-Alexandru Darvariu, Stephen Hailes et al.

An often neglected issue in multi-agent reinforcement learning (MARL) is the potential presence of unreliable agents in the environment whose deviations from expected behavior can prevent a system from accomplishing its intended tasks. In particular, consensus is a fundamental underpinning problem of cooperative distributed multi-agent systems. Consensus requires different agents, situated in a decentralized communication network, to reach an agreement out of a set of initial proposals that they put forward. Learning-based agents should adopt a protocol that allows them to reach consensus despite having one or more unreliable agents in the system. This paper investigates the problem of unreliable agents in MARL, considering consensus as a case study. Echoing established results in the distributed systems literature, our experiments show that even a moderate fraction of such agents can greatly impact the ability of reaching consensus in a networked environment. We propose Reinforcement Learning-based Trusted Consensus (RLTC), a decentralized trust mechanism, in which agents can independently decide which neighbors to communicate with. We empirically demonstrate that our trust mechanism is able to handle unreliable agents effectively, as evidenced by higher consensus success rates.

Nayana Dasgupta, Mirco Musolesi

Solving the problem of cooperation is fundamentally important for the creation and maintenance of functional societies. Problems of cooperation are omnipresent within human society, with examples ranging from navigating busy road junctions to negotiating treaties. As the use of AI becomes more pervasive throughout society, the need for socially intelligent agents capable of navigating these complex cooperative dilemmas is becoming increasingly evident. Direct punishment is a ubiquitous social mechanism that has been shown to foster the emergence of cooperation in both humans and non-humans. In the natural world, direct punishment is often strongly coupled with partner selection and reputation and used in conjunction with third-party punishment. The interactions between these mechanisms could potentially enhance the emergence of cooperation within populations. However, no previous work has evaluated the learning dynamics and outcomes emerging from Multi-Agent Reinforcement Learning (MARL) populations that combine these mechanisms. This paper addresses this gap. It presents a comprehensive analysis and evaluation of the behaviors and learning dynamics associated with direct punishment, third-party punishment, partner selection, and reputation. Finally, we discuss the implications of using these mechanisms on the design of cooperative AI systems.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Network flow problems, which involve distributing traffic such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics. Among them, the general Multi-Commodity Network Flow (MCNF) problem concerns the distribution of multiple flows of different sizes between several sources and sinks, while achieving effective utilization of the links. Due to the appeal of data-driven optimization, these problems have increasingly been approached using graph learning methods. In this paper, we propose a novel graph learning architecture for network flow problems called Per-Edge Weights (PEW). This method builds on a Graph Attention Network and uses distinctly parametrized message functions along each link. We extensively evaluate the proposed solution through an Internet flow routing case study using $17$ Service Provider topologies and $2$ routing schemes. We show that PEW yields substantial gains over architectures whose global message function constrains the routing unnecessarily. We also find that an MLP is competitive with other standard architectures. Furthermore, we analyze the relationship between graph structure and predictive performance for data-driven routing of flows, an aspect that has not been considered by existing work in the area.

Francesco De Lellis, Marco Coraggio, Giovanni Russo et al.

One of the major challenges in Deep Reinforcement Learning for control is the need for extensive training to learn the policy. Motivated by this, we present the design of the Control-Tutored Deep Q-Networks (CT-DQN) algorithm, a Deep Reinforcement Learning algorithm that leverages a control tutor, i.e., an exogenous control law, to reduce learning time. The tutor can be designed using an approximate model of the system, without any assumption about the knowledge of the system's dynamics. There is no expectation that it will be able to achieve the control objective if used stand-alone. During learning, the tutor occasionally suggests an action, thus partially guiding exploration. We validate our approach on three scenarios from OpenAI Gym: the inverted pendulum, lunar lander, and car racing. We demonstrate that CT-DQN is able to achieve better or equivalent data efficiency with respect to the classic function approximation solutions.

James Rudd-Jones, Mirco Musolesi, María Pérez-Ortiz

Chaotic dynamical systems pose a fundamental challenge for Reinforcement Learning (RL): exponential sensitivity to initial conditions induces high-variance bootstrap targets and poorly conditioned gradient updates. Chaotic dynamics arise across scientific and engineering domains, from fluid flows and climate systems to multi-agent systems, where reliable learning is highly desirable. Standard RL methods optimise expected returns through scalar value functions, implicitly averaging over diverging trajectories and entangling trajectory level instability with the learning objective. We show that under mild statistical stability assumptions, the return distribution evolves more regularly than individual trajectories when measured under the $1$-Wasserstein metric, yielding a smoother distributional Bellman objective. By aligning optimisation with this measure level structure, distributional RL provides better conditioned learning. We offer a principled explanation for the advantages of distributional methods in chaotic systems and the geometries of RL objectives under chaos.

Edmund R. Hunt, Chris Baber, Mehdi Sobhani et al.

Defining and measuring trust in dynamic, multiagent teams is important in a range of contexts, particularly in defense and security domains. Team members should be trusted to work towards agreed goals and in accordance with shared values. In this paper, our concern is with the definition of goals and values such that it is possible to define 'trust' in a way that is interpretable, and hence usable, by both humans and robots. We argue that the outcome of team activity can be considered in terms of 'goal', 'individual/team values', and 'legal principles'. We question whether alignment is possible at the level of 'individual/team values', or only at the 'goal' and 'legal principles' levels. We argue for a set of metrics to define trust in human-robot teams that are interpretable by human or robot team members, and consider an experiment that could demonstrate the notion of 'satisficing trust' over the course of a simulated mission.

Christoffel Doorman, Victor-Alexandru Darvariu, Stephen Hailes et al.

A key problem in network theory is how to reconfigure a graph in order to optimize a quantifiable objective. Given the ubiquity of networked systems, such work has broad practical applications in a variety of situations, ranging from drug and material design to telecommunications. The large decision space of possible reconfigurations, however, makes this problem computationally intensive. In this paper, we cast the problem of network rewiring for optimizing a specified structural property as a Markov Decision Process (MDP), in which a decision-maker is given a budget of modifications that are performed sequentially. We then propose a general approach based on the Deep Q-Network (DQN) algorithm and graph neural networks (GNNs) that can efficiently learn strategies for rewiring networks. We then discuss a cybersecurity case study, i.e., an application to the computer network reconfiguration problem for intrusion protection. In a typical scenario, an attacker might have a (partial) map of the system they plan to penetrate; if the network is effectively "scrambled", they would not be able to navigate it since their prior knowledge would become obsolete. This can be viewed as an entropy maximization problem, in which the goal is to increase the surprise of the network. Indeed, entropy acts as a proxy measurement of the difficulty of navigating the network topology. We demonstrate the general ability of the proposed method to obtain better entropy gains than random rewiring on synthetic and real-world graphs while being computationally inexpensive, as well as being able to generalize to larger graphs than those seen during training. Simulations of attack scenarios confirm the effectiveness of the learned rewiring strategies.

Giovanni Minelli, Mirco Musolesi

Robust coordination skills enable agents to operate cohesively in shared environments, together towards a common goal and, ideally, individually without hindering each other's progress. To this end, this paper presents Coordinated QMIX (CoMIX), a novel training framework for decentralized agents that enables emergent coordination through flexible policies, allowing at the same time independent decision-making at individual level. CoMIX models selfish and collaborative behavior as incremental steps in each agent's decision process. This allows agents to dynamically adapt their behavior to different situations balancing independence and collaboration. Experiments using a variety of simulation environments demonstrate that CoMIX outperforms baselines on collaborative tasks. The results validate our incremental approach as effective technique for improving coordination in multi-agent systems.

Francesco De Lellis, Marco Coraggio, Giovanni Russo et al.

In addressing control problems such as regulation and tracking through reinforcement learning, it is often required to guarantee that the acquired policy meets essential performance and stability criteria such as a desired settling time and steady-state error prior to deployment. Motivated by this necessity, we present a set of results and a systematic reward shaping procedure that (i) ensures the optimal policy generates trajectories that align with specified control requirements and (ii) allows to assess whether any given policy satisfies them. We validate our approach through comprehensive numerical experiments conducted in two representative environments from OpenAI Gym: the Inverted Pendulum swing-up problem and the Lunar Lander. Utilizing both tabular and deep reinforcement learning methods, our experiments consistently affirm the efficacy of our proposed framework, highlighting its effectiveness in ensuring policy adherence to the prescribed control requirements.

Lorenz Wolf, Mirco Musolesi

Existing modular Reinforcement Learning (RL) architectures are generally based on reusable components, also allowing for "plug-and-play" integration. However, these modules are homogeneous in nature - in fact, they essentially provide policies obtained via RL through the maximization of individual reward functions. Consequently, such solutions still lack the ability to integrate and process multiple types of information (i.e., heterogeneous knowledge representations), such as rules, sub-goals, and skills from various sources. In this paper, we discuss several practical examples of heterogeneous knowledge and propose Augmented Modular Reinforcement Learning (AMRL) to address these limitations. Our framework uses a selector to combine heterogeneous modules and seamlessly incorporate different types of knowledge representations and processing mechanisms. Our results demonstrate the performance and efficiency improvements, also in terms of generalization, that can be achieved by augmenting traditional modular RL with heterogeneous knowledge sources and processing mechanisms. Finally, we examine the safety, robustness, and interpretability issues stemming from the introduction of knowledge heterogeneity.

Olivia Macmillan-Scott, Mirco Musolesi

The concept of rationality is central to the field of artificial intelligence (AI). Whether we are seeking to simulate human reasoning, or trying to achieve bounded optimality, our goal is generally to make artificial agents as rational as possible. Despite the centrality of the concept within AI, there is no unified definition of what constitutes a rational agent. This article provides a survey of rationality and irrationality in AI, and sets out the open questions in this area. We consider how the understanding of rationality in other fields has influenced its conception within AI, in particular work in economics, philosophy and psychology. Focusing on the behaviour of artificial agents, we examine irrational behaviours that can prove to be optimal in certain scenarios. Some methods have been developed to deal with irrational agents, both in terms of identification and interaction, however work in this area remains limited. Methods that have up to now been developed for other purposes, namely adversarial scenarios, may be adapted to suit interactions with artificial agents. We further discuss the interplay between human and artificial agents, and the role that rationality plays within this interaction; many questions remain in this area, relating to potentially irrational behaviour of both humans and artificial agents.

Giorgio Franceschelli, Mirco Musolesi

Large language models (LLMs), particularly when integrated into agentic systems, have demonstrated human- and even superhuman-level performance across multiple domains. Whether these systems can truly be considered creative, however, remains a matter of debate, as conclusions heavily depend on the definitions, evaluation methods, and specific use cases employed. In this paper, we analyse creativity along two complementary macro-level perspectives. The first is a functionalist perspective, focusing on the observable characteristics of creative outputs. The second is an ontological perspective, emphasising the underlying processes, as well as the social and personal dimensions involved in creativity. We focus on LLM agents and we argue that they exhibit functionalist creativity, albeit not at its most sophisticated levels, while they continue to lack key aspects of ontological creativity. Finally, we discuss whether it is desirable for agentic systems to attain both forms of creativity, evaluating potential benefits and risks, and proposing pathways toward artificial creativity that can enhance human society.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Identifying causal structure is central to many fields ranging from strategic decision-making to biology and economics. In this work, we propose CD-UCT, a model-based reinforcement learning method for causal discovery based on tree search that builds directed acyclic graphs incrementally. We also formalize and prove the correctness of an efficient algorithm for excluding edges that would introduce cycles, which enables deeper discrete search and sampling in DAG space. The proposed method can be applied broadly to causal Bayesian networks with both discrete and continuous random variables. We conduct a comprehensive evaluation on synthetic and real-world datasets, showing that CD-UCT substantially outperforms the state-of-the-art model-free reinforcement learning technique and greedy search, constituting a promising advancement for combinatorial methods.

Alexei Pisacane, Victor-Alexandru Darvariu, Mirco Musolesi

Graph path search is a classic computer science problem that has been recently approached with Reinforcement Learning (RL) due to its potential to outperform prior methods. Existing RL techniques typically assume a global view of the network, which is not suitable for large-scale, dynamic, and privacy-sensitive settings. An area of particular interest is search in social networks due to its numerous applications. Inspired by seminal work in experimental sociology, which showed that decentralized yet efficient search is possible in social networks, we frame the problem as a collaborative task between multiple agents equipped with a limited local view of the network. We propose a multi-agent approach for graph path search that successfully leverages both homophily and structural heterogeneity. Our experiments, carried out over synthetic and real-world social networks, demonstrate that our model significantly outperforms learned and heuristic baselines. Furthermore, our results show that meaningful embeddings for graph navigation can be constructed using reward-driven learning.

Giorgio Franceschelli, Claudia Cevenini, Mirco Musolesi

The training process of foundation models as for other classes of deep learning systems is based on minimizing the reconstruction error over a training set. For this reason, they are susceptible to the memorization and subsequent reproduction of training samples. In this paper, we introduce a training-as-compressing perspective, wherein the model's weights embody a compressed representation of the training data. From a copyright standpoint, this point of view implies that the weights can be considered a reproduction or, more likely, a derivative work of a potentially protected set of works. We investigate the technical and legal challenges that emerge from this framing of the copyright of outputs generated by foundation models, including their implications for practitioners and researchers. We demonstrate that adopting an information-centric approach to the problem presents a promising pathway for tackling these emerging complex legal issues.

Gatis Mikelsons, Matthew Smith, Abhinav Mehrotra et al.

There is an increasing interest in exploiting mobile sensing technologies and machine learning techniques for mental health monitoring and intervention. Researchers have effectively used contextual information, such as mobility, communication and mobile phone usage patterns for quantifying individuals' mood and wellbeing. In this paper, we investigate the effectiveness of neural network models for predicting users' level of stress by using the location information collected by smartphones. We characterize the mobility patterns of individuals using the GPS metrics presented in the literature and employ these metrics as input to the network. We evaluate our approach on the open-source StudentLife dataset. Moreover, we discuss the challenges and trade-offs involved in building machine learning models for digital mental health and highlight potential future work in this direction.

Carla Griffiths, Mirco Musolesi

Understanding how linguistic structure emerges in language models is central to interpreting what these systems learn from data and how much supervision they truly require. In particular, semantic role understanding ("who did what to whom") is a core component of meaning representation, yet it remains unclear whether it arises from pre-training alone or depends on task-specific fine-tuning. We study whether semantic role understanding emerges during language model pre-training or requires task-specific fine-tuning. We freeze decoder-only transformers and train linear probes to extract semantic roles, using performance to infer whether role information is already encoded in pre-training or learned during adaptation. Across model scales, we find that frozen representations contain substantial semantic role information, with performance improving but not fully matching fine-tuned models. This indicates partial but incomplete emergence from pre-training alone. We show that semantic role structure emerges from language modeling objectives, but its internal implementation shifts toward more distributed representations as model scale increases.

Olivia Macmillan-Scott, Mirco Musolesi

Do large language models (LLMs) display rational reasoning? LLMs have been shown to contain human biases due to the data they have been trained on; whether this is reflected in rational reasoning remains less clear. In this paper, we answer this question by evaluating seven language models using tasks from the cognitive psychology literature. We find that, like humans, LLMs display irrationality in these tasks. However, the way this irrationality is displayed does not reflect that shown by humans. When incorrect answers are given by LLMs to these tasks, they are often incorrect in ways that differ from human-like biases. On top of this, the LLMs reveal an additional layer of irrationality in the significant inconsistency of the responses. Aside from the experimental results, this paper seeks to make a methodological contribution by showing how we can assess and compare different capabilities of these types of models, in this case with respect to rational reasoning.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures, are often challenging due to the rapid growth of the solution space. The trial-and-error paradigm of Reinforcement Learning has recently emerged as a promising alternative to traditional methods, such as exact algorithms and (meta)heuristics, for discovering better decision-making strategies in a variety of disciplines including chemistry, computer science, and statistics. Despite the fact that they arose in markedly different fields, these techniques share significant commonalities. Therefore, we set out to synthesize this work in a unifying perspective that we term Graph Reinforcement Learning, interpreting it as a constructive decision-making method for graph problems. After covering the relevant technical background, we review works along the dividing line of whether the goal is to optimize graph structure given a process of interest, or to optimize the outcome of the process itself under fixed graph structure. Finally, we discuss the common challenges facing the field and open research questions. In contrast with other surveys, the present work focuses on non-canonical graph problems for which performant algorithms are typically not known and Reinforcement Learning is able to provide efficient and effective solutions.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Causal structure discovery from observations can be improved by integrating background knowledge provided by an expert to reduce the hypothesis space. Recently, Large Language Models (LLMs) have begun to be considered as sources of prior information given the low cost of querying them relative to a human expert. In this work, firstly, we propose a set of metrics for assessing LLM judgments for causal graph discovery independently of the downstream algorithm. Secondly, we systematically study a set of prompting designs that allows the model to specify priors about the structure of the causal graph. Finally, we present a general methodology for the integration of LLM priors in graph discovery algorithms, finding that they help improve performance on common-sense benchmarks and especially when used for assessing edge directionality. Our work highlights the potential as well as the shortcomings of the use of LLMs in this problem space.

Giorgio Franceschelli, Mirco Musolesi

Large language models are revolutionizing several areas, including artificial creativity. However, the process of generation in machines profoundly diverges from that observed in humans. In particular, machine generation is characterized by a lack of intentionality and an underlying creative process. We propose a method called Creative Beam Search that uses Diverse Beam Search and LLM-as-a-Judge to perform response generation and response validation. The results of a qualitative experiment show how our approach can provide better output than standard sampling techniques. We also show that the response validation step is a necessary complement to the response generation step.

Elizaveta Tennant, Stephen Hailes, Mirco Musolesi

Increasing interest in ensuring the safety of next-generation Artificial Intelligence (AI) systems calls for novel approaches to embedding morality into autonomous agents. This goal differs qualitatively from traditional task-specific AI methodologies. In this paper, we provide a systematization of existing approaches to the problem of introducing morality in machines - modelled as a continuum. Our analysis suggests that popular techniques lie at the extremes of this continuum - either being fully hard-coded into top-down, explicit rules, or entirely learned in a bottom-up, implicit fashion with no direct statement of any moral principle (this includes learning from human feedback, as applied to the training and finetuning of large language models, or LLMs). Given the relative strengths and weaknesses of each type of methodology, we argue that more hybrid solutions are needed to create adaptable and robust, yet controllable and interpretable agentic systems. To that end, this paper discusses both the ethical foundations (including deontology, consequentialism and virtue ethics) and implementations of morally aligned AI systems. We present a series of case studies that rely on intrinsic rewards, moral constraints or textual instructions, applied to either pure-Reinforcement Learning or LLM-based agents. By analysing these diverse implementations under one framework, we compare their relative strengths and shortcomings in developing morally aligned AI systems. We then discuss strategies for evaluating the effectiveness of moral learning agents. Finally, we present open research questions and implications for the future of AI safety and ethics which are emerging from this hybrid framework.

Charles Westphal, Stephen Hailes, Mirco Musolesi

Network Intrusion Detection (NID) remains a key area of research within the information security community, while also being relevant to Machine Learning (ML) practitioners. The latter generally aim to detect attacks using network features, which have been extracted from raw network data typically using dimensionality reduction methods, such as principal component analysis (PCA). However, PCA is not able to assess the relevance of features for the task at hand. Consequently, the features available are of varying quality, with some being entirely non-informative. From this, two major drawbacks arise. Firstly, trained and deployed models have to process large amounts of unnecessary data, therefore draining potentially costly resources. Secondly, the noise caused by the presence of irrelevant features can, in some cases, impede a model's ability to detect an attack. In order to deal with these challenges, we present Feature Selection for Network Intrusion Detection (FSNID) a novel information-theoretic method that facilitates the exclusion of non-informative features when detecting network intrusions. The proposed method is based on function approximation using a neural network, which enables a version of our approach that incorporates a recurrent layer. Consequently, this version uniquely enables the integration of temporal dependencies. Through an extensive set of experiments, we demonstrate that the proposed method selects a significantly reduced feature set, while maintaining NID performance. Code will be made available upon publication.

Charles Westphal, Stephen Hailes, Mirco Musolesi

Pruning has emerged as the primary approach used to limit the resource requirements of large neural networks (NNs). Since the proposal of the lottery ticket hypothesis, researchers have focused either on pruning at initialization or after training. However, recent theoretical findings have shown that the sample efficiency of robust pruned models is proportional to the mutual information (MI) between the pruning masks and the model's training datasets, \textit{whether at initialization or after training}. In this paper, starting from these results, we introduce Mutual Information Preserving Pruning (MIPP), a structured activation-based pruning technique applicable before or after training. The core principle of MIPP is to select nodes in a way that conserves MI shared between the activations of adjacent layers, and consequently between the data and masks. Approaching the pruning problem in this manner means we can prove that there exists a function that can map the pruned upstream layer's activations to the downstream layer's, implying re-trainability. We demonstrate that MIPP consistently outperforms state-of-the-art methods, regardless of whether pruning is performed before or after training.

Elizaveta Tennant, Stephen Hailes, Mirco Musolesi

Growing concerns about safety and alignment of AI systems highlight the importance of embedding moral capabilities in artificial agents: a promising solution is the use of learning from experience, i.e., Reinforcement Learning. In multi-agent (social) environments, complex population-level phenomena may emerge from interactions between individual learning agents. Many of the existing studies rely on simulated social dilemma environments to study the interactions of independent learning agents; however, they tend to ignore the moral heterogeneity that is likely to be present in societies of agents in practice. For example, at different points in time a single learning agent may face opponents who are consequentialist (i.e., focused on maximizing outcomes over time), norm-based (i.e., conforming to specific norms), or virtue-based (i.e., considering a combination of different virtues). The extent to which agents' co-development may be impacted by such moral heterogeneity in populations is not well understood. In this paper, we present a study of the learning dynamics of morally heterogeneous populations interacting in a social dilemma setting. Using an Iterated Prisoner's Dilemma environment with a partner selection mechanism, we investigate the extent to which the prevalence of diverse moral agents in populations affects individual agents' learning behaviors and emergent population-level outcomes. We observe several types of non-trivial interactions between pro-social and anti-social agents, and find that certain types of moral agents are able to steer selfish agents towards more cooperative behavior.

Giorgio Franceschelli, Mirco Musolesi

Despite their growing capabilities, language models still frequently reproduce content from their training data, generate repetitive text, and favor common grammatical patterns and vocabulary. A possible cause is the decoding strategy: the most common strategies either consider only the most probable tokens, which reduces output diversity, or increase the likelihood of unlikely tokens, compromising output accuracy and correctness. In this paper, we propose DiffSampling, a new decoding method that leverages a mathematical analysis of the token probability distribution to ensure the generation of contextually appropriate text. In particular, the difference between consecutive, sorted probabilities can be used to truncate incorrect tokens. In addition, we also propose two variations of the proposed method that aim to correct the subtle inconsistencies of common sampling strategies. Experiments involving four different text-generation tasks demonstrate that our approach consistently performs at least on par with the existing methods it builds upon in terms of quality, while potentially improving output diversity.

Charles Westphal, Stephen Hailes, Mirco Musolesi

The Information Bottleneck (IB) principle offers a compelling theoretical framework to understand how neural networks (NNs) learn. However, its practical utility has been constrained by unresolved theoretical ambiguities and significant challenges in accurate estimation. In this paper, we present a \textit{Generalized Information Bottleneck (GIB)} framework that reformulates the original IB principle through the lens of synergy, i.e., the information obtainable only through joint processing of features. We provide theoretical and empirical evidence demonstrating that synergistic functions achieve superior generalization compared to their non-synergistic counterparts. Building on these foundations we re-formulate the IB using a computable definition of synergy based on the average interaction information (II) of each feature with those remaining. We demonstrate that the original IB objective is upper bounded by our GIB in the case of perfect estimation, ensuring compatibility with existing IB theory while addressing its limitations. Our experimental results demonstrate that GIB consistently exhibits compression phases across a wide range of architectures (including those with \textit{ReLU} activations where the standard IB fails), while yielding interpretable dynamics in both CNNs and Transformers and aligning more closely with our understanding of adversarial robustness.

Lorenz Wolf, Robert Kirk, Mirco Musolesi

Reinforcement learning from human feedback (RLHF) is a widely used method for aligning large language models with human preferences. However, RLHF often suffers from reward model overoptimisation, in which models overfit to the reward function, resulting in non-generalisable policies that exploit the idiosyncrasies and peculiarities of the reward function. A common mitigation is iterated RLHF, in which reward models are repeatedly retrained with updated human feedback and policies are re-optimised. Despite its increasing adoption, the dynamics of overoptimisation in this setting remain poorly understood. In this work, we present the first comprehensive study of overoptimisation in iterated RLHF. We systematically analyse key design choices - how reward model training data is transferred across iterations, which reward function is used for optimisation, and how policies are initialised. Using the controlled AlpacaFarm benchmark, we observe that overoptimisation tends to decrease over successive iterations, as reward models increasingly approximate ground-truth preferences. However, performance gains diminish over time, and while reinitialising from the base policy is robust, it limits optimisation flexibility. Other initialisation strategies often fail to recover from early overoptimisation. These findings offer actionable insights for building more stable and generalisable RLHF pipelines.

James Rudd-Jones, Mirco Musolesi, María Pérez-Ortiz

Climate policy development faces significant challenges due to deep uncertainty, complex system dynamics, and competing stakeholder interests. Climate simulation methods, such as Earth System Models, have become valuable tools for policy exploration. However, their typical use is for evaluating potential polices, rather than directly synthesizing them. The problem can be inverted to optimize for policy pathways, but the traditional optimization approaches often struggle with non-linear dynamics, heterogeneous agents, and comprehensive uncertainty quantification. We propose a framework for augmenting climate simulations with Multi-Agent Reinforcement Learning (MARL) to address these limitations. We identify key challenges at the interface between climate simulations and the application of MARL in the context of policy synthesis, including reward definition, scalability with increasing agents and state spaces, uncertainty propagation across linked systems, and solution validation. Additionally, we discuss challenges in making MARL-derived solutions interpretable and useful for policy-makers. Our framework provides a foundation for more sophisticated climate policy exploration while acknowledging important limitations and areas for future research.

Alec Sargood, Lemuel Puglisi, Elinor Thompson et al.

Tractography is the process of inferring the trajectories of white-matter pathways in the brain from diffusion magnetic resonance imaging (dMRI). Local tractography methods, which construct streamlines by following local fiber orientation estimates stepwise through an image, are prone to error accumulation and high false positive rates, particularly on noisy or low-resolution data. In contrast, global methods, which attempt to optimize a collection of streamlines to maximize compatibility with underlying fiber orientation estimates, are computationally expensive. To address these challenges, we introduce GenTract, the first generative model for global tractography. We frame tractography as a generative task, learning a direct mapping from dMRI to complete, anatomically plausible streamlines. We compare both diffusion-based and flow matching paradigms and evaluate GenTract's performance against state-of-the-art baselines. Notably, GenTract achieves precision 2.1x higher than the next-best method, TractOracle. This advantage becomes even more pronounced in challenging low-resolution and noisy settings, where it outperforms the closest competitor by an order of magnitude. By producing tractograms with high precision on research-grade data while also maintaining reliability on imperfect, lower-resolution data, GenTract represents a promising solution for global tractography.

Marta Emili Garcia Segura, Stephen Hailes, Mirco Musolesi

Large Language Models (LLMs) are increasingly being deployed as autonomous agents in real-world environments. As these deployments scale, multi-agent interactions become inevitable, making it essential to understand strategic behavior in such systems. A central open question is whether LLM agents, like reinforcement learning agents, can shape the learning dynamics and influence the behavior of others through interaction alone. In this paper, we present the first investigation of opponent shaping (OS) with LLM-based agents. Existing OS algorithms cannot be directly applied to LLMs, as they require higher-order derivatives, face scalability constraints, or depend on architectural components that are absent in transformers. To address this gap, we introduce ShapeLLM, an adaptation of model-free OS methods tailored for transformer-based agents. Using ShapeLLM, we examine whether LLM agents can influence co-players' learning dynamics across diverse game-theoretic environments. We demonstrate that LLM agents can successfully guide opponents toward exploitable equilibria in competitive games (Iterated Prisoner's Dilemma, Matching Pennies, and Chicken) and promote coordination and improve collective welfare in cooperative games (Iterated Stag Hunt and a cooperative version of the Prisoner's Dilemma). Our findings show that LLM agents can both shape and be shaped through interaction, establishing opponent shaping as a key dimension of multi-agent LLM research.

Luca Serfilippi, Giorgio Franceschelli, Antonio Corradi et al.

Policy gradient methods often balance exploitation and exploration via entropy maximization. However, maximizing entropy pushes the policy towards a uniform random distribution, which represents an unstructured and sometimes inefficient exploration strategy. In this work, we propose replacing the entropy bonus with a more robust complexity bonus. In particular, we adopt a measure of complexity, defined as the product of Shannon entropy and disequilibrium, where the latter quantifies the distance from the uniform distribution. This regularizer encourages policies that balance stochasticity (high entropy) with structure (high disequilibrium), guiding agents toward regimes where useful, non-trivial behaviors can emerge. Such behaviors arise because the regularizer suppresses both extremes, e.g., maximal disorder and complete order, creating pressure for agents to discover structured yet adaptable strategies. Starting from Proximal Policy Optimization (PPO), we introduce Complexity-Driven Policy Optimization (CDPO), a new learning algorithm that replaces entropy with complexity. We show empirically across a range of discrete action space tasks that CDPO is more robust to the choice of the complexity coefficient than PPO is with the entropy coefficient, especially in environments requiring greater exploration.

Giorgio Franceschelli, Mirco Musolesi

Despite the increasing use of large language models for creative tasks, their outputs often lack diversity. Common solutions, such as sampling at higher temperatures, can compromise the quality of the results. Dealing with this trade-off is still an open challenge in designing AI systems for creativity. Drawing on information theory, we propose a context-based score to quantitatively evaluate value and originality. This score incentivizes accuracy and adherence to the request while fostering divergence from the learned distribution. We show that our score can be used as a reward in a reinforcement learning framework to fine-tune large language models for maximum performance. We validate our strategy through experiments considering a variety of creative tasks, such as poetry generation and math problem solving, demonstrating that it enhances the value and originality of the generated solutions.

Giorgio Franceschelli, Mirco Musolesi

The Overfitted Brain hypothesis suggests dreams happen to allow generalization in the human brain. Here, we ask if the same is true for reinforcement learning agents as well. Given limited experience in a real environment, we use imagination-based reinforcement learning to train a policy on dream-like episodes, where non-imaginative, predicted trajectories are modified through generative augmentations. Experiments on four ProcGen environments show that, compared to classic imagination and offline training on collected experience, our method can reach a higher level of generalization when dealing with sparsely rewarded environments.

Charles Westphal, Stephen Hailes, Mirco Musolesi

Identifying the most suitable variables to represent the state is a fundamental challenge in Reinforcement Learning (RL). These variables must efficiently capture the information necessary for making optimal decisions. In order to address this problem, in this paper, we introduce the Transfer Entropy Redundancy Criterion (TERC), an information-theoretic criterion, which determines if there is \textit{entropy transferred} from state variables to actions during training. We define an algorithm based on TERC that provably excludes variables from the state that have no effect on the final performance of the agent, resulting in more sample efficient learning. Experimental results show that this speed-up is present across three different algorithm classes (represented by tabular Q-learning, Actor-Critic, and Proximal Policy Optimization (PPO)) in a variety of environments. Furthermore, to highlight the differences between the proposed methodology and the current state-of-the-art feature selection approaches, we present a series of controlled experiments on synthetic data, before generalizing to real-world decision-making tasks. We also introduce a representation of the problem that compactly captures the transfer of information from state variables to actions as Bayesian networks.

Giorgio Franceschelli, Mirco Musolesi

Measuring machine creativity is one of the most fascinating challenges in Artificial Intelligence. This paper explores the possibility of using generative learning techniques for automatic assessment of creativity. The proposed solution does not involve human judgement, it is modular and of general applicability. We introduce a new measure, namely DeepCreativity, based on Margaret Boden's definition of creativity as composed by value, novelty and surprise. We evaluate our methodology (and related measure) considering a case study, i.e., the generation of 19th century American poetry, showing its effectiveness and expressiveness.

Alberto Jesu, Victor-Alexandru Darvariu, Alessandro Staffolani et al.

The growing number of applications of Reinforcement Learning (RL) in real-world domains has led to the development of privacy-preserving techniques due to the inherently sensitive nature of data. Most existing works focus on differential privacy, in which information is revealed in the clear to an agent whose learned model should be robust against information leakage to malicious third parties. Motivated by use cases in which only encrypted data might be shared, such as information from sensitive sites, in this work we consider scenarios in which the inputs themselves are sensitive and cannot be revealed. We develop a simple extension to the MDP framework which provides for the encryption of states. We present a preliminary, experimental study of how a DQN agent trained on encrypted states performs in environments with discrete and continuous state spaces. Our results highlight that the agent is still capable of learning in small state spaces even in presence of non-deterministic encryption, but performance collapses in more complex environments.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

We tackle the problem of goal-directed graph construction: given a starting graph, a budget of modifications, and a global objective function, the aim is to find a set of edges whose addition to the graph achieves the maximum improvement in the objective (e.g., communication efficiency). This problem emerges in many networks of great importance for society such as transportation and critical infrastructure networks. We identify two significant shortcomings with present methods. Firstly, they focus exclusively on network topology while ignoring spatial information; however, in many real-world networks, nodes are embedded in space, which yields different global objectives and governs the range and density of realizable connections. Secondly, existing RL methods scale poorly to large networks due to the high cost of training a model and the scaling factors of the action space and global objectives. In this work, we formulate this problem as a deterministic MDP. We adopt the Monte Carlo Tree Search framework for planning in this domain, prioritizing the optimality of final solutions over the speed of policy evaluation. We propose several improvements over the standard UCT algorithm for this family of problems, addressing their single-agent nature, the trade-off between the costs of edges and their contribution to the objective, and an action space linear in the number of nodes. We demonstrate the suitability of this approach for improving the global efficiency and attack resilience of a variety of synthetic and real-world networks, including Internet backbone networks and metro systems. Our approach obtains a 24% improvement in these metrics compared to UCT on the largest networks tested and scalability superior to previous methods.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Public goods games represent insightful settings for studying incentives for individual agents to make contributions that, while costly for each of them, benefit the wider society. In this work, we adopt the perspective of a central planner with a global view of a network of self-interested agents and the goal of maximizing some desired property in the context of a best-shot public goods game. Existing algorithms for this known NP-complete problem find solutions that are sub-optimal and cannot optimize for criteria other than social welfare. In order to efficiently solve public goods games, our proposed method directly exploits the correspondence between equilibria and the Maximal Independent Set (mIS) structural property of graphs. In particular, we define a Markov Decision Process which incrementally generates an mIS, and adopt a planning method to search for equilibria, outperforming existing methods. Furthermore, we devise a graph imitation learning technique that uses demonstrations of the search to obtain a graph neural network parametrized policy which quickly generalizes to unseen game instances. Our evaluation results show that this policy is able to reach 99.5% of the performance of the planning method while being three orders of magnitude faster to evaluate on the largest graphs tested. The methods presented in this work can be applied to a large class of public goods games of potentially high societal impact and more broadly to other graph combinatorial optimization problems.

Giorgio Franceschelli, Mirco Musolesi

Machine-generated artworks are now part of the contemporary art scene: they are attracting significant investments and they are presented in exhibitions together with those created by human artists. These artworks are mainly based on generative deep learning techniques, which have seen a formidable development and remarkable refinement in the very recent years. Given the inherent characteristics of these techniques, a series of novel legal problems arise. In this article, we consider a set of key questions in the area of generative deep learning for the arts, including the following: is it possible to use copyrighted works as training set for generative models? How do we legally store their copies in order to perform the training process? Who (if someone) will own the copyright on the generated data? We try to answer these questions considering the law in force in both the United States of America and the European Union, and potential future alternatives. We then extend our analysis to code generation, which is an emerging area of generative deep learning. Finally, we also formulate a set of practical guidelines for artists and developers working on deep learning generated art, as well as some policy suggestions for policymakers.

Giorgio Franceschelli, Mirco Musolesi

There is a growing interest in the area of machine learning and creativity. This survey presents an overview of the history and the state of the art of computational creativity theories, key machine learning techniques (including generative deep learning), and corresponding automatic evaluation methods. After presenting a critical discussion of the key contributions in this area, we outline the current research challenges and emerging opportunities in this field.

Nicolas Anastassacos, Julian García, Stephen Hailes et al.

Creating incentives for cooperation is a challenge in natural and artificial systems. One potential answer is reputation, whereby agents trade the immediate cost of cooperation for the future benefits of having a good reputation. Game theoretical models have shown that specific social norms can make cooperation stable, but how agents can independently learn to establish effective reputation mechanisms on their own is less understood. We use a simple model of reinforcement learning to show that reputation mechanisms generate two coordination problems: agents need to learn how to coordinate on the meaning of existing reputations and collectively agree on a social norm to assign reputations to others based on their behavior. These coordination problems exhibit multiple equilibria, some of which effectively establish cooperation. When we train agents with a standard Q-learning algorithm in an environment with the presence of reputation mechanisms, convergence to undesirable equilibria is widespread. We propose two mechanisms to alleviate this: (i) seeding a proportion of the system with fixed agents that steer others towards good equilibria; and (ii), intrinsic rewards based on the idea of introspection, i.e., augmenting agents' rewards by an amount proportionate to the performance of their own strategy against themselves. A combination of these simple mechanisms is successful in stabilizing cooperation, even in a fully decentralized version of the problem where agents learn to use and assign reputations simultaneously. We show how our results relate to the literature in Evolutionary Game Theory, and discuss implications for artificial, human and hybrid systems, where reputations can be used as a way to establish trust and cooperation.

Mariflor Vega-Carrasco, Jason O'sullivan, Rosie Prior et al.

Understanding the shopping motivations behind market baskets has high commercial value in the grocery retail industry. Analyzing shopping transactions demands techniques that can cope with the volume and dimensionality of grocery transactional data while keeping interpretable outcomes. Latent Dirichlet Allocation (LDA) provides a suitable framework to process grocery transactions and to discover a broad representation of customers' shopping motivations. However, summarizing the posterior distribution of an LDA model is challenging, while individual LDA draws may not be coherent and cannot capture topic uncertainty. Moreover, the evaluation of LDA models is dominated by model-fit measures which may not adequately capture the qualitative aspects such as interpretability and stability of topics. In this paper, we introduce clustering methodology that post-processes posterior LDA draws to summarise the entire posterior distribution and identify semantic modes represented as recurrent topics. Our approach is an alternative to standard label-switching techniques and provides a single posterior summary set of topics, as well as associated measures of uncertainty. Furthermore, we establish a more holistic definition for model evaluation, which assesses topic models based not only on their likelihood but also on their coherence, distinctiveness and stability. By means of a survey, we set thresholds for the interpretation of topic coherence and topic similarity in the domain of grocery retail data. We demonstrate that the selection of recurrent topics through our clustering methodology not only improves model likelihood but also outperforms the qualitative aspects of LDA such as interpretability and stability. We illustrate our methods on an example from a large UK supermarket chain.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.

Alessio Pagani, Abhinav Mehrotra, Mirco Musolesi

Understanding and learning the characteristics of network paths has been of particular interest for decades and has led to several successful applications. Such analysis becomes challenging for urban networks as their size and complexity are significantly higher compared to other networks. The state-of-the-art machine learning (ML) techniques allow us to detect hidden patterns and, thus, infer the features associated with them. However, very little is known about the impact on the performance of such predictive models by the use of different input representations. In this paper, we design and evaluate six different graph input representations (i.e., representations of the network paths), by considering the network's topological and temporal characteristics, for being used as inputs for machine learning models to learn the behavior of urban networks paths. The representations are validated and then tested with a real-world taxi journeys dataset predicting the tips using a road network of New York. Our results demonstrate that the input representations that use temporal information help the model to achieve the highest accuracy (RMSE of 1.42$).

Nicolas Anastassacos, Stephen Hailes, Mirco Musolesi

Social dilemmas have been widely studied to explain how humans are able to cooperate in society. Considerable effort has been invested in designing artificial agents for social dilemmas that incorporate explicit agent motivations that are chosen to favor coordinated or cooperative responses. The prevalence of this general approach points towards the importance of achieving an understanding of both an agent's internal design and external environment dynamics that facilitate cooperative behavior. In this paper, we investigate how partner selection can promote cooperative behavior between agents who are trained to maximize a purely selfish objective function. Our experiments reveal that agents trained with this dynamic learn a strategy that retaliates against defectors while promoting cooperation with other agents resulting in a prosocial society.