迈向Tsallis完全概率设计
Towards Tsallis Fully Probabilistic Design
AI总结：
本文提出基于Tsallis散度的完全概率设计框架，用于处理非高斯尾部行为的随机过程，通过双迭代方案证明了其收敛性与最优性。
摘要：
完全概率设计（FPD）是一种强大的框架，提供了随机控制、学习和决策的优雅统一描述。本文引入了广义的FPD框架，称为Tsallis FPD。Tsallis FPD使用Tsallis散度替代标准FPD中的Kullback-Leibler散度。Tsallis散度是非广泛统计力学的自然推广，为具有非高斯尾部行为的随机过程提供灵活性。在构建Tsallis FPD后，我们通过固定点迭代法证明了其收敛性。该构造采用双迭代方案，执行一系列逆向归纳，而非传统FPD中单次向下传递的步骤。我们证明了该构造渐近收敛到固定点，并且该固定点是Tsallis FPD的最优解。
英文摘要：
Fully Probabilistic design (FPD) is a powerful framework offering an elegant and unifying account of stochastic control, learning and decision-making. Here we introduce a generalized FPD framework, which we term as Tsallis FPD. Tsallis FPD uses Tsallis divergence in place of the Kullback-Leibler divergence that defines the standard FPD cost term. Tsallis divergence is a natural generalization of the KL divergence, rooted in non-extensive statistical mechanics and providing flexibility towards modeling stochastic processes with non-Gaussian tail behavior. After formulating Tsallis FPD, we present a double iteration scheme that performs a sequence of backwards inductions, rather than a single pass down the stages that constitutes the proven approach for classical FPD.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
