Interpreting systems as solving POMDPs: a step towards a formal understanding of agency

TL;DR

This paper proposes a formal framework to interpret systems as agents solving POMDPs, linking beliefs, goals, and actions to better understand agency in physical systems.

Contribution

It extends existing interpretation maps to include goals and actions using POMDP theory, providing a formal definition of agency.

Findings

Systems can be interpreted as POMDP solutions with belief-based actions

This approach links physical states to agency-related features

Provides a step towards a formal understanding of agency

Abstract

Under what circumstances can a system be said to have beliefs and goals, and how do such agency-related features relate to its physical state? Recent work has proposed a notion of interpretation map, a function that maps the state of a system to a probability distribution representing its beliefs about an external world. Such a map is not completely arbitrary, as the beliefs it attributes to the system must evolve over time in a manner that is consistent with Bayes' theorem, and consequently the dynamics of a system constrain its possible interpretations. Here we build on this approach, proposing a notion of interpretation not just in terms of beliefs but in terms of goals and actions. To do this we make use of the existing theory of partially observable Markov processes (POMDPs): we say that a system can be interpreted as a solution to a POMDP if it not only admits an interpretation map describing its beliefs about the hidden state of a POMDP but also takes actions that are optimal according to its belief state. An agent is then a system together with an interpretation of this system as a POMDP solution. Although POMDPs are not the only possible formulation of what it means to have a goal, this nevertheless represents a step towards a more general formal definition of what it means for a system to be an agent.