Optimal Search Strategies under Finite Resource Constraints: The Role of Environmental Memory and Directional Information in Informed and Blind Protocols
Abstract
Improving the efficiency of a stochastic search often requires to provide the searching agent with resources that modify its dynamics and help it explore space more quickly. Although such resources are often assumed to be unlimited and treated as a cost to mitigate, many realistic search processes operate under a finite resource budget, e.g. in processes with environmental memory in which the searcher deposits long-lasting cues along its path that it can interact with at later times to guide its further search. Here, we address the question of how to allocate a limited budget to maximize search efficiency by investigating a one-dimensional diffusing agent whose access to resources is constrained. We consider three resource models, namely an external force applied by an external controller to pull the searcher towards the target, directional flags deposited by the searcher along its path that redirect its motion towards the target, and self-generated chemorepulsive cues that act as a force field. For all these models, we find that resource usage should be concentrated in narrow regions of space when information about the searcher's current and past positions is available. In contrast, in blind strategies where a predefined time protocol is followed, resources should be used at a steady rate to ensure it to be used at most of its capacity by the time it reaches the target. We further show that blind strategies in non-Markovian processes with environmental memory are significantly less efficient due to the inherent fluctuations in the locations of deposited cues.
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BibTeX
@misc{meyer2026optimal,
title = {{Optimal Search Strategies under Finite Resource Constraints: The Role of Environmental Memory and Directional Information in Informed and Blind Protocols}},
author = {Hugues Meyer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31244},
eprint = {2610.31244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31244},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal Search Strategies under Finite Resource Constraints: The Role of Environmental Memory and Directional Information in Informed and Blind Protocols
AU - Hugues Meyer
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31244
UR - https://arxiv.org/abs/2610.31244
AB - Improving the efficiency of a stochastic search often requires to provide the searching agent with resources that modify its dynamics and help it explore space more quickly. Although such resources are often assumed to be unlimited and treated as a cost to mitigate, many realistic search processes operate under a finite resource budget, e.g. in processes with environmental memory in which the searcher deposits long-lasting cues along its path that it can interact with at later times to guide its further search. Here, we address the question of how to allocate a limited budget to maximize search efficiency by investigating a one-dimensional diffusing agent whose access to resources is constrained. We consider three resource models, namely an external force applied by an external controller to pull the searcher towards the target, directional flags deposited by the searcher along its path that redirect its motion towards the target, and self-generated chemorepulsive cues that act as a force field. For all these models, we find that resource usage should be concentrated in narrow regions of space when information about the searcher's current and past positions is available. In contrast, in blind strategies where a predefined time protocol is followed, resources should be used at a steady rate to ensure it to be used at most of its capacity by the time it reaches the target. We further show that blind strategies in non-Markovian processes with environmental memory are significantly less efficient due to the inherent fluctuations in the locations of deposited cues.
ER -