Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning
This work provides an alternative theoretical framework for understanding complexity in processes like multi-arm bandits, which is incremental as it builds on existing analyses without introducing new methods or data.
The paper analyzes the structural complexity of infinite-memory processes constructed from random samples of stationary, ergodic finite-memory components, contrasting with computational and statistical approaches to reveal relationships between predictability, complexity, and learning, highlighting divergences in informational and correlational aspects.
We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. Such processes are familiar from the well known multi-arm Bandit problem. We contrast our analysis with computation-theoretic and statistical inference approaches to understanding their complexity. The result is an alternative view of the relationship between predictability, complexity, and learning that highlights the distinct ways in which informational and correlational divergences arise in complex ergodic and nonergodic processes. We draw out consequences for the resource divergences that delineate the structural hierarchy of ergodic processes and for processes that are themselves hierarchical.