The World Is Bigger! A Computationally-Embedded Perspective on the Big World Hypothesis
This work addresses the problem of designing agents that can continually adapt in complex, unbounded environments, which is incremental as it builds on existing continual learning frameworks with a new formal perspective.
The paper tackles the challenge of continual learning under the big world hypothesis by introducing a computationally-embedded perspective, proving it is equivalent to an agent in a partially observable Markov decision process with infinite states, and showing that deep linear networks sustain higher interactivity than deep nonlinear networks as capacity increases.
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.