Grau-Moya Jordi, Krüger Matthias, Braun Daniel A
Max Planck Institute for Intelligent Systems, Stuttgart 70569, Germany.
Max Planck Institute for Biological Cybernetics, Tübingen 72076, Germany.
Entropy (Basel). 2017 Dec 21;20(1):1. doi: 10.3390/e20010001.
Living organisms from single cells to humans need to adapt continuously to respond to changes in their environment. The process of behavioural adaptation can be thought of as improving decision-making performance according to some utility function. Here, we consider an abstract model of organisms as decision-makers with limited information-processing resources that trade off between maximization of utility and computational costs measured by a relative entropy, in a similar fashion to thermodynamic systems undergoing isothermal transformations. Such systems minimize the free energy to reach equilibrium states that balance internal energy and entropic cost. When there is a fast change in the environment, these systems evolve in a non-equilibrium fashion because they are unable to follow the path of equilibrium distributions. Here, we apply concepts from non-equilibrium thermodynamics to characterize decision-makers that adapt to changing environments under the assumption that the temporal evolution of the utility function is externally driven and does not depend on the decision-maker's action. This allows one to quantify performance loss due to imperfect adaptation in a general manner and, additionally, to find relations for decision-making similar to Crooks' fluctuation theorem and Jarzynski's equality. We provide simulations of several exemplary decision and inference problems in the discrete and continuous domains to illustrate the new relations.
从单细胞生物到人类，所有生物都需要不断适应以应对环境变化。行为适应过程可以被看作是根据某种效用函数来提高决策性能。在此，我们将生物视为具有有限信息处理资源的决策者，构建一个抽象模型，这些决策者在效用最大化和以相对熵衡量的计算成本之间进行权衡，类似于经历等温变换的热力学系统。此类系统通过最小化自由能来达到平衡状态，该平衡状态平衡了内能和熵成本。当环境发生快速变化时，这些系统以非平衡方式演化，因为它们无法遵循平衡分布的路径。在此，我们应用非平衡热力学的概念来刻画决策者，这些决策者在效用函数的时间演化由外部驱动且不依赖于决策者行动的假设下适应不断变化的环境。这使得人们能够以一种通用方式量化由于不完全适应导致的性能损失，此外，还能找到类似于克鲁克斯涨落定理和雅津斯基等式的决策关系。我们提供了离散和连续域中几个示例性决策和推理问题的模拟，以说明这些新关系。
