Zipf's Law as a necessary condition for mitigating the scaling problem in rule-based agents.

摘要

The scaling problem arises when linear growth in some agent feature demands faster-than-linear growth in the consumption of a scarce input. This inquiry models information-processing agents as classifier systems with fixed-length, fixed-position, constant-specificity rules, and under constant, conservative external physical force. It proves that as such systems grow linearly in the number of rules they employ, their energy demands necessarily grow faster than linear, leading to the scaling problem. It also proves that energy-converting systems can minimize dissipation during conversion by following the Principle of Least Action from Physics. Under this principle, a necessary condition for energy-converting systems under conservative force is that the first-order change in the magnitude of their action, the time integral of the difference between energy forms, is zero under small changes in their behavior or path . When the principle is applied to the classifier-system information-processing agent created here, it causes a hyperbolic Pareto histogram known as Zipf's Law and serves to provide a deterministic model to explain the origin of this law.