Chemotaxis emerges as the optimal solution to cooperative search games

TL;DR

This paper reveals that optimal cooperative search strategies are mathematically equivalent to chemotaxis models, providing a biophysical perspective on decision-making and offering insights for optimizing search algorithms.

Contribution

It establishes a novel analogy between cooperative search strategies and chemotaxis, linking decision-making parameters to biochemical processes and explaining the effectiveness of chemotaxis-inspired algorithms.

Findings

Optimal search strategies mirror chemotaxis equations

Biochemical processes relate to decision-making parameters

Chemotaxis-inspired algorithms can be optimized based on this analogy

Abstract

Cooperative search games are collective tasks where all agents share the same goal of reaching a target in the shortest time while limiting energy expenditure and avoiding collisions. Here we show that the equations that characterize the optimal strategy are identical to a long-known phenomenological model of chemotaxis, the directed motion of microorganisms guided by chemical cues. Within this analogy, the substance to which searchers respond acts as the memory over which agents share information about the environment. The actions of writing, erasing and forgetting are equivalent to production, consumption and degradation of chemoattractant. The rates at which these biochemical processes take place are tightly related to the parameters that characterize the decision-making problem, such as learning rate, costs for time, control, collisions and their trade-offs, as well as the attitude of agents toward risk. We establish a dictionary that maps notions from decision-making theory to biophysical observables in chemotaxis, and vice versa. Our results offer a fundamental explanation of why search algorithms that mimic microbial chemotaxis can be very effective and suggest how to optimize their performance.