A "good regulator theorem" for embodied agents

2025-08-04

AI Summary

The Conant–Ashby “good regulator theorem”—which posits that every good regulator of a system must be a model of that system—lacks generality in embodied agents, particularly when internal explicit models are absent. Method: We propose an observer-driven generalized notion of “model,” redefining it as an external observer’s updateable belief structure about the environment, inferred from the agent’s behavior, rather than an internal explicit representation. Grounded in information theory and Bayesian inference, and informed by artificial life behavioral analysis, we formally characterize the existence of equivalent environmental models in regulation tasks. Contribution/Results: Our framework unifies explanations for effective regulation without internal models, transcending traditional control-theoretic constraints on model implementation. It provides a more general and interpretable theoretical foundation for modeling embodied intelligence, reconciling observed adaptive behavior with minimal representational assumptions.

Technology Category

• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Multiagent Systems: Modeling other Agents
• Intelligent Robots: Embodied AI

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Generalizing Conant and Ashby's good regulator theorem for embodied agents
• Defining belief-updating as a more sophisticated model notion
• Resolving apparent counterexamples with observer-imposed models

Innovation

• Observer interprets agent's beliefs as models
• Belief updating defines sophisticated model notion
• Theorem applies broadly to regulation tasks