Categorical Internalisation of Environmental Groupoids for Generalisable POMDP Solving
TL;DR
This paper advocates category theory as a practical framework for structuring and improving rein- forcement learning in high-dimensional, partially observable environments by partitioning the state space into equivalence classes induced by sym- metry orbits, and organising each such class as a groupoid with a designated canonical representative.
Abstract
This paper advocates category theory as a practical framework for structuring and improving rein- forcement learning in high-dimensional, partially observable environments. We model symmetries between environmental states by partitioning the state space into equivalence classes induced by sym- metry orbits, and organise each such class as a groupoid with a designated canonical representative. This allows the agent to share what it learns across many similar environmental states simultaneously, rather than treating every orientation or position as an entirely new problem. Learning is thus carried out on a symmetry-reduced state space with each orbit represented once, preserving structure while eliminating redundancy and improving sample efficiency. We implement this framework within standard reinforcement learning pipelines and evaluate two different approaches on partially observable benchmarks, demonstrating that orbit-based partitioning yields consistent performance improvements in environments exhibiting latent symmetry. Beyond these empirical results, our approach illustrates how categorical structure provides a principled bridge between abstract reinforcement learning formulations and their computational application, thereby establishing a pathway toward more structured and scalable learning systems.
