A "good regulator theorem" for embodied agents

TL;DR

This paper extends the good regulator theorem by framing regulation as belief updating, emphasizing the observer's role in interpreting agents' behavior as having models of their environment, applicable to both external and internal regulation.

Contribution

It introduces a broader, observer-dependent formulation of the good regulator theorem based on belief updating, applicable to diverse regulation scenarios.

Findings

Agents performing regulation can be interpreted as having beliefs about their environment.

The observer's perspective is essential in defining models of the system.

The theorem applies to both external environment regulation and internal state regulation.

Abstract

In a classic paper, Conant and Ashby claimed that "every good regulator of a system must be a model of that system." Artificial Life has produced many examples of systems that perform tasks with apparently no model in sight; these suggest Conant and Ashby's theorem doesn't easily generalise beyond its restricted setup. Nevertheless, here we show that a similar intuition can be fleshed out in a different way: whenever an agent is able to perform a regulation task, it is possible for an observer to interpret it as having "beliefs" about its environment, which it "updates" in response to sensory input. This notion of belief updating provides a notion of model that is more sophisticated than Conant and Ashby's, as well as a theorem that is more broadly applicable. However, it necessitates a change in perspective, in that the observer plays an essential role in the theory: models are not a mere property of the system but are imposed on it from outside. Our theorem holds regardless of whether the system is regulating its environment in a classic control theory setup, or whether it's regulating its own internal state; the model is of its environment either way. The model might be trivial, however, and this is how the apparent counterexamples are resolved.