Universal Decision Models

TL;DR

This paper introduces Universal Decision Models (UDMs), a category-theoretic formalism that unifies various decision-making frameworks, enabling advanced analysis and abstraction of complex decision tasks across disciplines.

Contribution

The paper presents a novel category-theoretic formalism for decision models that generalizes existing frameworks like MDPs and game theory, with algorithms for minimal object computation.

Findings

UDMs unify diverse decision models under a single formalism

Universal properties like information integration and decision solvability are formulated

An algorithm for minimal object computation in UDMs is proposed

Abstract

Humans are universal decision makers: we reason causally to understand the world; we act competitively to gain advantage in commerce, games, and war; and we are able to learn to make better decisions through trial and error. In this paper, we propose Universal Decision Model (UDM), a mathematical formalism based on category theory. Decision objects in a UDM correspond to instances of decision tasks, ranging from causal models and dynamical systems such as Markov decision processes and predictive state representations, to network multiplayer games and Witsenhausen's intrinsic models, which generalizes all these previous formalisms. A UDM is a category of objects, which include decision objects, observation objects, and solution objects. Bisimulation morphisms map between decision objects that capture structure-preserving abstractions. We formulate universal properties of UDMs, including information integration, decision solvability, and hierarchical abstraction. We describe universal functorial representations of UDMs, and propose an algorithm for computing the minimal object in a UDM using algebraic topology. We sketch out an application of UDMs to causal inference in network economics, using a complex multiplayer producer-consumer two-sided marketplace.