Theory for Optimal Estimation and Control under Resource Limitations and Its Applications to Biological Information Processing and Decision-Making
arXiv:2409.14003 · doi:10.1103/gvl6-cvby
Abstract
Despite being optimized, the information processing of biological organisms exhibits significant variability in its complexity and capability. One potential source of this diversity is the limitation of resources required for information processing. However, we lack a theoretical framework that comprehends the relationship between biological information processing and resource limitations and integrates it with decision-making conduced downstream of the information processing. In this paper, we propose a novel optimal estimation and control theory that accounts for the resource limitations inherent in biological systems. This theory explicitly formulates the memory that organisms can store and operate and obtains optimal memory dynamics using optimal control theory. This approach takes account of various resource limitations, such as memory capacity, intrinsic noise, and energy cost, and unifies state estimation and control. We apply this theory to minimal models of biological information processing and decision-making under resource limitations and find that such limitations induce discontinuous and non-monotonic phase transitions between memory-less and memory-based strategies. Therefore, this theory establishes a comprehensive framework for addressing biological information processing and decision-making under resource limitations, revealing the rich and complex behaviors that arise from resource limitations.
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