Factored Value Functions for Graph-Based Multi-Agent Reinforcement Learning

Credit assignment is a core challenge in multi-agent reinforcement learning (MARL), especially in large-scale systems with structured, local interactions. Graph-based Markov decision processes (GMDPs) capture such settings via an influence graph, but standard critics are poorly aligned with this structure: global value functions provide weak per-agent learning signals, while existing local constructions can be difficult to estimate and ill-behaved in infinite-horizon settings. We introduce the Diffusion Value Function (DVF), a factored value function for GMDPs that assigns to each agent a value component by diffusing rewards over the influence graph with temporal discounting and spatial attenuation. We show that DVF is well-defined, admits a Bellman fixed point, and decomposes the global discounted value via an averaging property. DVF can be used as a drop-in critic in standard RL algorithms and estimated scalably with graph neural networks. Building on DVF, we propose Diffusion A2C (DA2C) and a sparse message-passing actor, Learned DropEdge GNN (LD-GNN), for learning decentralised algorithms under communication costs. Across the firefighting benchmark and three distributed computation tasks (vector graph colouring and two transmit power optimisation problems), DA2C consistently outperforms local and global critic baselines, improving average reward by up to 11%.

Enhancing Dynamic CT Image Reconstruction with Neural Fields Through Explicit Motion Regularizers

Image reconstruction for dynamic inverse problems with highly undersampled data poses a major challenge: not accounting for the dynamics of the process leads to a non-realistic motion with no time regularity. Variational approaches that penalize time derivatives or introduce motion model regularizers have been proposed to relate subsequent frames and improve image quality using grid-based discretization. Neural fields offer an alternative parametrization of the desired spatiotemporal quantity with a deep neural network, a lightweight, continuous, and biased towards smoothness representation. The inductive bias has been exploited to enforce time regularity for dynamic inverse problems resulting in neural fields optimized by minimizing a data-fidelity term only. In this paper we investigate and show the benefits of introducing explicit PDE-based motion regularizers, namely, the optical flow equation, in 2D+time computed tomography for the optimization of neural fields. We also compare neural fields against a grid-based solver and show that the former outperforms the latter.