In this paper we present the foundations of Fully Probabilistic Design for the case when the Kullback-Leibler divergence is replaced by the Tsallis divergence. Because the standard chain rule is replaced by subadditivity, immediate backwards recursion is not available. However, by forming a fixed point iteration, we can establish a constructive proof of the existence of a solution to this problem, which also constitutes an algorithmic scheme that iteratively converges to this solution. This development can provide greater versatility in Bayesian Decision Making as far as adding flexibility to the problem formulation.

翻译：本文提出了当Kullback-Leibler散度被Tsallis散度替代时的完全概率设计理论基础。由于标准链式法则被次可加性替代，无法直接进行反向递归。然而，通过构建不动点迭代，我们能够建立该问题解存在性的构造性证明，这同时构成了迭代收敛至该解的算法框架。这一进展可为贝叶斯决策提供更强的灵活性，从而增强问题表述的适应能力。