Towards Foundations of Categorical Cybernetics

TL;DR

This paper introduces a categorical framework for modeling bidirectional interactive processes like open learners and compositional game theory, aiming to establish a foundational understanding of cybernetic systems.

Contribution

It develops a novel categorical approach to formalize processes involving environment and controller interactions, unifying concepts from open learners and game theory.

Findings

Framework successfully models open learners and game-theoretic agents

Provides a unified formal basis for cybernetic processes

Enhances understanding of bidirectional process interactions

Abstract

We propose a categorical framework for processes which interact bidirectionally with both an environment and a 'controller'. Examples include open learners, in which the controller is an optimiser such as gradient descent, and an approach to compositional game theory closely related to open games, in which the controller is a composite of game-theoretic agents. We believe that 'cybernetic' is an appropriate name for the processes that can be described in this framework.