General Agents Contain World Models, even under Partial Observability and Stochasticity

TL;DR

This paper proves that even stochastic, partially observable agents inherently contain models of their environment, extending previous results that were limited to deterministic, fully observable agents, thus highlighting the fundamental nature of world models.

Contribution

It extends the theoretical framework to show that stochastic and partially observable agents must contain world models, weakening assumptions and broadening applicability.

Findings

Stochastic agents contain approximate world models.

Partially observable environments do not prevent agents from modeling.

Weaker notions of generality still imply the presence of world models.

Abstract

Deciding whether an agent possesses a model of its surrounding world is a fundamental step toward understanding its capabilities and limitations. In [10], it was shown that, within a particular framework, every almost optimal and general agent necessarily contains sufficient knowledge of its environment to allow an approximate reconstruction of it by querying the agent as a black box. This result relied on the assumptions that the agent is deterministic and that the environment is fully observable. In this work, we remove both assumptions by extending the theorem to stochastic agents operating in partially observable environments. Fundamentally, this shows that stochastic agents cannot avoid learning their environment through the usage of randomization. We also strengthen the result by weakening the notion of generality, proving that less powerful agents already contain a model of the world in which they operate.