Theory for Optimal Estimation and Control under Resource Limitations and Its Applications to Biological Information Processing and Decision-Making

TL;DR

This paper develops a novel optimal estimation and control framework that explicitly incorporates resource limitations like memory, noise, and energy costs, explaining complex behaviors in biological information processing and decision-making.

Contribution

It introduces a unified theoretical approach to model biological information processing under resource constraints, linking memory dynamics with decision strategies.

Findings

Resource limitations induce phase transitions between memoryless and memory-based strategies.

The theory unifies estimation and control in resource-constrained biological systems.

Complex behaviors emerge from resource limitations in biological information processing.

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.