L\'evy walks derived from a Bayesian decision-making model in non-stationary environments

TL;DR

This paper demonstrates that learning and forgetting in Bayesian decision-making models can produce Le9vy walk patterns, explaining migratory behaviors observed in nature.

Contribution

It introduces a novel Bayesian inference algorithm incorporating learning and forgetting, linking confidence dynamics to Le9vy walk emergence in non-stationary environments.

Findings

Learning induces high-confidence states leading to Le9vy walks.

Forgetting alone results in Brownian motion with low confidence.

Mixture of confidence states explains Le9vy walk patterns.

Abstract

L\'evy walks are found in the migratory behaviour patterns of various organisms, and the reason for this phenomenon has been much discussed. We use simulations to demonstrate that learning causes the changes in confidence level during decision-making in non-stationary environments, and results in L\'evy-walk-like patterns. One inference algorithm involving confidence is Bayesian inference. We propose an algorithm that introduces the effects of learning and forgetting into Bayesian inference, and simulate an imitation game in which two decision-making agents incorporating the algorithm estimate each other's internal models from their opponent's observational data. For forgetting without learning, agent confidence levels remained low due to a lack of information on the counterpart and Brownian walks occurred for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and Brownian walks universally became L\'evy walks through a mixture of high- and low-confidence states.