In this paper, we study the collaborative learning model, which concerns the tradeoff between parallelism and communication overhead in multi-agent multi-armed bandits. For regret minimization in multi-armed bandits, we present the first set of tradeoffs between the number of rounds of communication among the agents and the regret of the collaborative learning process.

The significance of the freshness of sensor and control data at the receiver side, often referred to as Age of Information (AoI), is fundamentally constrained by contention for limited network resources. Evidently, network congestion is detrimental for AoI, where this congestion is partly self-induced by the sensor transmission process in addition to the contention from other transmitting sensors. In this work, we devise a decentralized AoI-minimizing transmission policy for a number of sensor agents sharing capacity-limited, non-FIFO duplex channels that introduce random delays in communication with a common receiver. By implementing the same policy, however with no explicit inter-agent communication, the agents minimize the expected AoI in this partially observable system. We cater to the partial observability due to random channel delays by designing a bootstrap particle filter that independently maintains a belief over the AoI of each agent. We also leverage mean-field control approximations and reinforcement learning to derive scalable and optimal solutions for minimizing the expected AoI collaboratively.

Widely considered a cornerstone of human morality, trust shapes many aspects of human social interactions. In this work, we present a theoretical analysis of the $\textit{trust game}$, the canonical task for studying trust in behavioral and brain sciences, along with simulation results supporting our analysis. Specifically, leveraging reinforcement learning (RL) to train our AI agents, we systematically investigate learning trust under various parameterizations of this task. Our theoretical analysis, corroborated by the simulations results presented, provides a mathematical basis for the emergence of trust in the trust game.

The behaviour of multi-agent learning in competitive network games is often studied within the context of zero-sum games, in which convergence guarantees may be obtained. However, outside of this class the behaviour of learning is known to display complex behaviours and convergence cannot be always guaranteed. Nonetheless, in order to develop a complete picture of the behaviour of multi-agent learning in competitive settings, the zero-sum assumption must be lifted. Motivated by this we study the Q-Learning dynamics, a popular model of exploration and exploitation in multi-agent learning, in competitive network games. We determine how the degree of competition, exploration rate and network connectivity impact the convergence of Q-Learning. To study generic competitive games, we parameterise network games in terms of correlations between agent payoffs and study the average behaviour of the Q-Learning dynamics across all games drawn from a choice of this parameter. This statistical approach establishes choices of parameters for which Q-Learning dynamics converge to a stable fixed point. Differently to previous works, we find that the stability of Q-Learning is explicitly dependent only on the network connectivity rather than the total number of agents. Our experiments validate these findings and show that, under certain network structures, the total number of agents can be increased without increasing the likelihood of unstable or chaotic behaviours.

This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate inference. To do so, we define on the `syntactic' side the new notion of Bayesian lens and show that Bayesian updating composes according to the compositional lens pattern. Using Bayesian lenses, and inspired by compositional game theory, we define fibrations of statistical games and classify various problems of statistical inference as corresponding sections: the chain rule of the relative entropy is formalized as a strict section, while maximum likelihood estimation and the free energy give lax sections. In the process, we introduce a new notion of `copy-composition'. On the `semantic' side, we present a new formalization of general open dynamical systems (particularly: deterministic, stochastic, and random; and discrete- and continuous-time) as certain coalgebras of polynomial functors, which we show collect into monoidal opindexed categories (or, alternatively, into algebras for multicategories of generalized polynomial functors). We use these opindexed categories to define monoidal bicategories of cilia: dynamical systems which control lenses, and which supply the target for our functorial semantics. Accordingly, we construct functors which explain the bidirectional compositional structure of predictive coding neural circuits under the free energy principle, thereby giving a formal mathematical underpinning to the bidirectionality observed in the cortex. Along the way, we explain how to compose rate-coded neural circuits using an algebra for a multicategory of linear circuit diagrams, showing subsequently that this is subsumed by lenses and polynomial functors.

Graph federated learning (FL) has emerged as a pivotal paradigm enabling multiple agents to collaboratively train a graph model while preserving local data privacy. Yet, current efforts overlook a key issue: agents are self-interested and would hesitant to share data without fair and satisfactory incentives. This paper is the first endeavor to address this issue by studying the incentive mechanism for graph federated learning. We identify a unique phenomenon in graph federated learning: the presence of agents posing potential harm to the federation and agents contributing with delays. This stands in contrast to previous FL incentive mechanisms that assume all agents contribute positively and in a timely manner. In view of this, this paper presents a novel incentive mechanism tailored for fair graph federated learning, integrating incentives derived from both model gradient and payoff. To achieve this, we first introduce an agent valuation function aimed at quantifying agent contributions through the introduction of two criteria: gradient alignment and graph diversity. Moreover, due to the high heterogeneity in graph federated learning, striking a balance between accuracy and fairness becomes particularly crucial. We introduce motif prototypes to enhance accuracy, communicated between the server and agents, enhancing global model aggregation and aiding agents in local model optimization. Extensive experiments show that our model achieves the best trade-off between accuracy and the fairness of model gradient, as well as superior payoff fairness.

An important real-world application of multi-robot systems is multi-robot patrolling (MRP), where robots must carry out the activity of going through an area at regular intervals. Motivations for MRP include the detection of anomalies that may represent security threats. While MRP algorithms show some maturity in development, a key potential advantage has been unexamined: the ability to exploit collective perception of detected anomalies to prioritize the location ordering of security checks. This is because noisy individual-level detection of an anomaly may be compensated for by group-level consensus formation regarding whether an anomaly is likely to be truly present. Here, we examine the performance of unmodified idleness-based patrolling algorithms when given the additional objective of reaching an environmental perception consensus via local pairwise communication and a quorum threshold. We find that generally, MRP algorithms that promote physical mixing of robots, as measured by a higher connectivity of their emergent communication network, reach consensus more quickly. However, when there is noise present in anomaly detection, a more moderate (constrained) level of connectivity is preferable because it reduces the spread of false positive detections, as measured by a group-level F-score. These findings can inform user choice of MRP algorithm and future algorithm development.

This paper addresses the problem of multi-agent pursuit, where slow pursuers cooperate to capture fast evaders in a confined environment with obstacles. Existing heuristic algorithms often lack expressive coordination strategies and are highly sensitive to task conditions, requiring extensive hyperparameter tuning. In contrast, reinforcement learning (RL) has been applied to this problem and is capable of obtaining cooperative pursuit strategies. However, RL-based methods face challenges in training for complex scenarios due to the vast amount of training data and limited adaptability to varying task conditions, such as different scene sizes, varying numbers and speeds of obstacles, and flexible speed ratios of the evader to the pursuer. In this work, we combine RL and curriculum learning to introduce a flexible solver for multiagent pursuit problems, named TaskFlex Solver (TFS), which is capable of solving multi-agent pursuit problems with diverse and dynamically changing task conditions in both 2-dimensional and 3-dimensional scenarios. TFS utilizes a curriculum learning method that constructs task distributions based on training progress, enhancing training efficiency and final performance. Our algorithm consists of two main components: the Task Evaluator, which evaluates task success rates and selects tasks of moderate difficulty to maintain a curriculum archive, and the Task Sampler, which constructs training distributions by sampling tasks from the curriculum archive to maximize policy improvement. Experiments show that TFS produces much stronger performance than baselines and achieves close to 100% capture rates in both 2-dimensional and 3-dimensional multi-agent pursuit problems with diverse and dynamically changing scenes. The project website is at https://sites.google.com/view/tfs-2023.

Traditional social learning frameworks consider environments with a homogeneous state, where each agent receives observations conditioned on that true state of nature. In this work, we relax this assumption and study the distributed hypothesis testing problem in a heterogeneous environment, where each agent can receive observations conditioned on their own personalized state of nature (or truth). This situation arises in many scenarios, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. In these heterogeneous contexts, the graph topology admits a block structure. We study social learning under personalized (or multitask) models and examine their convergence behavior.

While decentralized training is attractive in multi-agent reinforcement learning (MARL) for its excellent scalability and robustness, its inherent coordination challenges in collaborative tasks result in numerous interactions for agents to learn good policies. To alleviate this problem, action advising methods make experienced agents share their knowledge about what to do, while less experienced agents strictly follow the received advice. However, this method of sharing and utilizing knowledge may hinder the team's exploration of better states, as agents can be unduly influenced by suboptimal or even adverse advice, especially in the early stages of learning. Inspired by the fact that humans can learn not only from the success but also from the failure of others, this paper proposes a novel knowledge sharing framework called Cautiously-Optimistic kNowledge Sharing (CONS). CONS enables each agent to share both positive and negative knowledge and cautiously assimilate knowledge from others, thereby enhancing the efficiency of early-stage exploration and the agents' robustness to adverse advice. Moreover, considering the continuous improvement of policies, agents value negative knowledge more in the early stages of learning and shift their focus to positive knowledge in the later stages. Our framework can be easily integrated into existing Q-learning based methods without introducing additional training costs. We evaluate CONS in several challenging multi-agent tasks and find it excels in environments where optimal behavioral patterns are difficult to discover, surpassing the baselines in terms of convergence rate and final performance.