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

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.

Harnessing Discrete Representations For Continual Reinforcement Learning

Reinforcement learning (RL) agents make decisions using nothing but observations from the environment, and consequently, heavily rely on the representations of those observations. Though some recent breakthroughs have used vector-based categorical representations of observations, often referred to as discrete representations, there is little work explicitly assessing the significance of such a choice. In this work, we provide a thorough empirical investigation of the advantages of representing observations as vectors of categorical values within the context of reinforcement learning. We perform evaluations on world-model learning, model-free RL, and ultimately continual RL problems, where the benefits best align with the needs of the problem setting. We find that, when compared to traditional continuous representations, world models learned over discrete representations accurately model more of the world with less capacity, and that agents trained with discrete representations learn better policies with less data. In the context of continual RL, these benefits translate into faster adapting agents. Additionally, our analysis suggests that the observed performance improvements can be attributed to the information contained within the latent vectors and potentially the encoding of the discrete representation itself.