Unifying Causal Inference and Reinforcement Learning using Higher-Order Category Theory

by   Sridhar Mahadevan, et al.
University of Massachusetts Amherst

We present a unified formalism for structure discovery of causal models and predictive state representation (PSR) models in reinforcement learning (RL) using higher-order category theory. Specifically, we model structure discovery in both settings using simplicial objects, contravariant functors from the category of ordinal numbers into any category. Fragments of causal models that are equivalent under conditional independence – defined as causal horns – as well as subsequences of potential tests in a predictive state representation – defined as predictive horns – are both special cases of horns of a simplicial object, subsets resulting from the removal of the interior and the face opposite a particular vertex. Latent structure discovery in both settings involve the same fundamental mathematical problem of finding extensions of horns of simplicial objects through solving lifting problems in commutative diagrams, and exploiting weak homotopies that define higher-order symmetries. Solutions to the problem of filling "inner" vs "outer" horns leads to various notions of higher-order categories, including weak Kan complexes and quasicategories. We define the abstract problem of structure discovery in both settings in terms of adjoint functors between the category of universal causal models or universal decision models and its simplicial object representation.


page 1

page 2

page 3

page 4


On The Universality of Diagrams for Causal Inference and The Causal Reproducing Property

We propose Universal Causality, an overarching framework based on catego...

Universal Decision Models

Humans are universal decision makers: we reason causally to understand t...

A Layered Architecture for Universal Causality

We propose a layered hierarchical architecture called UCLA (Universal Ca...

Causality in Higher Order Process Theories

Quantum supermaps provide a framework in which higher order quantum proc...

Causal models in string diagrams

The framework of causal models provides a principled approach to causal ...

A Mathematical Framework for Transformations of Physical Processes

We observe that the existence of sequential and parallel composition sup...

Percolation in higher order networks via mapping to chygraphs

Percolation theory investigates systems of interconnected units, their r...

Please sign up or login with your details

Forgot password? Click here to reset