Gottwald Sebastian, Braun Daniel A
Institute of Neural Information Processing, Ulm University, 89081 Ulm, Germany.
Entropy (Basel). 2019 Apr 6;21(4):375. doi: 10.3390/e21040375.
In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can be reduced is limited by the amount of available computational resources. Here, we introduce the notion of elementary computation based on a fundamental principle for probability transfers that reduce uncertainty. Elementary computations can be considered as the inverse of Pigou-Dalton transfers applied to probability distributions, closely related to the concepts of majorization, T-transforms, and generalized entropies that induce a preorder on the space of probability distributions. Consequently, we can define resource cost functions that are order-preserving and therefore monotonic with respect to the uncertainty reduction. This leads to a comprehensive notion of decision-making processes with limited resources. Along the way, we prove several new results on majorization theory, as well as on entropy and divergence measures.
在其最基本的形式中，决策可以被视为一个逐步消除备选方案从而减少不确定性的计算过程。此类过程通常成本高昂，这意味着能够减少的不确定性量受到可用计算资源量的限制。在此，我们基于减少不确定性的概率转移基本原理引入基本计算的概念。基本计算可被视为应用于概率分布的庇古 - 道尔顿转移的逆运算，与在概率分布空间上诱导预序的优化、T变换和广义熵的概念密切相关。因此，我们可以定义保持序的资源成本函数，从而相对于不确定性减少是单调的。这导致了具有有限资源的决策过程的综合概念。在此过程中，我们证明了关于优化理论以及熵和散度度量的几个新结果。
