The World Is Bigger! A Computationally-Embedded Perspective on the Big World Hypothesis

TL;DR

This paper introduces a formal framework for understanding continual learning through the lens of an embedded automaton within an environment, emphasizing the importance of adaptability over fixed solutions.

Contribution

It formalizes the concept of an embedded agent as an automaton in a universal computer, linking it to POMDPs, and proposes an interactivity objective for continual learning evaluation.

Findings

Deep nonlinear networks struggle to sustain interactivity.

Deep linear networks maintain higher interactivity with increased capacity.

The proposed model-based RL algorithm effectively evaluates continual learning capabilities.

Abstract

Continual learning is often motivated by the idea, known as the big world hypothesis, that "the world is bigger" than the agent. Recent problem formulations capture this idea by explicitly constraining an agent relative to the environment. These constraints lead to solutions in which the agent continually adapts to best use its limited capacity, rather than converging to a fixed solution. However, explicit constraints can be ad hoc, difficult to incorporate, and may limit the effectiveness of scaling up the agent's capacity. In this paper, we characterize a problem setting in which an agent, regardless of its capacity, is constrained by being embedded in the environment. In particular, we introduce a computationally-embedded perspective that represents an embedded agent as an automaton simulated within a universal (formal) computer. Such an automaton is always constrained; we prove that it is equivalent to an agent that interacts with a partially observable Markov decision process over a countably infinite state-space. We propose an objective for this setting, which we call interactivity, that measures an agent's ability to continually adapt its behaviour by learning new predictions. We then develop a model-based reinforcement learning algorithm for interactivity-seeking, and use it to construct a synthetic problem to evaluate continual learning capability. Our results show that deep nonlinear networks struggle to sustain interactivity, whereas deep linear networks sustain higher interactivity as capacity increases.