Complexity as Advantage: A Regret-Based Perspective on Emergent Structure
This provides a quantitative grounding for why complexity is valuable, with implications for learning, evolution, and AI, though it appears incremental in refining existing complexity theories.
The paper tackles the problem of defining system complexity by proposing Complexity as Advantage (CAA), a framework that measures complexity based on predictive regret across different observers, showing it unifies notions like multiscale entropy and predictive information.
We introduce Complexity as Advantage (CAA), a framework that defines the complexity of a system relative to a family of observers. Instead of measuring complexity as an intrinsic property, we evaluate how much predictive regret a system induces for different observers attempting to model it. A system is complex when it is easy for some observers and hard for others, creating an information advantage. We show that this formulation unifies several notions of emergent behavior, including multiscale entropy, predictive information, and observer-dependent structure. The framework suggests that "interesting" systems are those positioned to create differentiated regret across observers, providing a quantitative grounding for why complexity can be functionally valuable. We demonstrate the idea through simple dynamical models and discuss implications for learning, evolution, and artificial agents.