Towards Tsallis Fully Probabilistic Design

Abstract

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.

In an earlier version, the manuscript claimed theoretical results that were later found to be mistaken. The existence of a solution to the Tsallis FPD problem, and the fixed point and convergence guarantees of the double loop scheme introduced are currently ongoing work