Category theory improves learning in complex partial observation environments
Categorical Internalisation of Environmental Groupoids for Generalisable POMDP Solving
Artificial Intelligence
Summary
Learning to act in a world where you can only see part of what’s happening is difficult, especially when many situations look very similar but appear different. The authors use a special math framework called category theory to group similar states together so the agent learns from many similar situations at once instead of starting fresh each time. This makes learning faster and more efficient by cutting down on repeated effort. They tested two ways to do this and found it consistently helps in robots or programs that must make decisions with limited information.
What this means in practice
- •For robotics engineers: Reduce training time for robots navigating environments where some details can’t be fully seen by grouping symmetrical states together for shared learning.
- •For video game developers: Improve AI agents’ learning efficiency in games with symmetrical or repetitive map features by leveraging symmetry to avoid redundant training.
Authors
Ben Opperman, Eduardo Alonso, Esther Mondragón
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.