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A Dynamical Systems Approach to Optimal Foraging

Siddharth Chaturvedi,Ahmed El-Gazzar,M. Gerven

Published 2024 in bioRxiv

ABSTRACT

Foraging for resources in an environment is a fundamental activity that must be addressed by any biological agent. Modelling this phenomenon in simulations can enhance our understanding of the characteristics of natural intelligence. In this work, we present a novel approach to model foraging in-silico using a continuous coupled dynamical system. The dynamical system is composed of three differential equations, representing the position of the agent, the agent’s control policy, and the environmental resource dynamics. Crucially, the control policy is implemented as a parameterized differential equation which allows the control policy to adapt in order to solve the foraging task. Using this setup, we show that when these dynamics are coupled and the controller parameters are optimized to maximize the rate of reward collected, adaptive foraging emerges in the agent. We further show that the internal dynamics of the controller, as a surrogate brain model, closely resemble the dynamics of the evidence accumulation mechanism, which may be used by certain neurons of the dorsal anterior cingulate cortex region in non-human primates, for deciding when to migrate from one patch to another. We show that by modulating the resource growth rates of the environment, the emergent behaviour of the artificial agent agrees with the predictions of the optimal foraging theory. Finally, we demonstrate how the framework can be extended to stochastic and multi-agent settings. Author Summary Intelligence is a phenomenon that arises due to the interactions of an agent’s dynamics with the environment’s dynamics under the assumption that the agent seeks optimization of certain objective. Modelling both these dynamics as a single coupled dynamical system can shed light on patterns of intelligence that unfold in time. This report aims to provide a minimal in-silico framework that models the main components involved in natural phenomena, like optimal foraging, as a coupled dynamical system. Interestingly, we observe similarities between the surrogate brain dynamics of the artificial agent with the evidence accumulation mechanism that can be responsible for decision-making in certain non-human primates performing a similar foraging task. We also observe similarities between trends prescribed by theories prevalent in behavioural ecology such as the optimal foraging theory and those shown by the artificial agent. Such similarities can increase the predictability and explainability of artificial systems. We can now expect them to mimic these natural decision-making mechanisms by replicating such trends and we can thus understand the reasoning behind their actions. They can also increase the confidence of researchers to consider using such artificial agent models as simulation tools to make predictions and test hypotheses about aspects of natural intelligence.

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