James Rudd-Jones

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.

James Rudd-Jones, Fiona Thendean, María Pérez-Ortiz

Climate change poses an existential threat, necessitating effective climate policies to enact impactful change. Decisions in this domain are incredibly complex, involving conflicting entities and evidence. In the last decades, policymakers increasingly use simulations and computational methods to guide some of their decisions. Integrated Assessment Models (IAMs) are one of such methods, which combine social, economic, and environmental simulations to forecast potential policy effects. For example, the UN uses outputs of IAMs for their recent Intergovernmental Panel on Climate Change (IPCC) reports. Traditionally these have been solved using recursive equation solvers, but have several shortcomings, e.g. struggling at decision making under uncertainty. Recent preliminary work using Reinforcement Learning (RL) to replace the traditional solvers shows promising results in decision making in uncertain and noisy scenarios. We extend on this work by introducing multiple interacting RL agents as a preliminary analysis on modelling the complex interplay of socio-interactions between various stakeholders or nations that drives much of the current climate crisis. Our findings show that cooperative agents in this framework can consistently chart pathways towards more desirable futures in terms of reduced carbon emissions and improved economy. However, upon introducing competition between agents, for instance by using opposing reward functions, desirable climate futures are rarely reached. Modelling competition is key to increased realism in these simulations, as such we employ policy interpretation by visualising what states lead to more uncertain behaviour, to understand algorithm failure. Finally, we highlight the current limitations and avenues for further work to ensure future technology uptake for policy derivation.

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.

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.