Theory for optimal estimation and control under resource limitations and its applications to biological information processing and decision-making

While the information processing of organisms is evolutionarily optimized, it exhibits remarkable diversity in its complexity and capability. One potential source of this diversity is the limitations of resources available for information processing. However, we still lack a theoretical framework that clarifies the relationship between biological information processing and resource limitations and integrates it with downstream decision-making. Together with the accompanying letter [Tottori and Kobayashi, ], this full paper presents an optimal estimation and control framework that explicitly incorporates resource limitations inherent in biological systems. While the accompanying letter focuses on the nontrivial phase transitions induced by resource limitations, the present full paper establishes the theoretical foundation and provides a comprehensive analysis of these transitions. The proposed framework formulates memory that organisms can store and operate, and optimizes it using optimal control theory. This approach accounts for various resource limitations—such as memory capacity, intrinsic noise, and energy cost—and unifies estimation and control. Applying this theory to minimal models of biological information processing and decision-making, we demonstrate that resource limitations can induce discontinuous and nonmonotonic phase transitions between memoryless and memory-based strategies. These results provide a comprehensive theoretical foundation for studying how organisms process information and make decisions under resource limitations, and suggest that the rich diversity observed in biological systems may emerge from such constraints.