Towards Foundations of Categorical Cybernetics

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.

arXiv commentIn Proceedings ACT 2021, arXiv:2211.01102

References in corpus (9)

• Coend calculus
• Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams
• Monoidal Grothendieck construction
• Profunctor Optics, a Categorical Update
• String Diagrams For Double Categories and Equipments
• Translating Extensive Form Games to Open Games with Agency
• Bayesian open games
• Backward Induction for Repeated Games
• Compositional Game Theory, Compositionally

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• A category theory framework for Bayesian learning
• Reinforcement Learning in Categorical Cybernetics
• String Diagrams with Factorized Densities
• On a fibrational construction for optics, lenses, and Dialectica categories
• Organizing Physics with Open Energy-Driven Systems
• A Category Theoretic Approach to Approximate Game Theory
• Approximate Inference via Fibrations of Statistical Games