  In this paper, we provide a generalized framework for Variational
Inference-Stochastic Optimal Control by using thenon-extensive Tsallis
divergence. By incorporating the deformed exponential function into the
optimality likelihood function, a novel Tsallis Variational Inference-Model
Predictive Control algorithm is derived, which includes prior works such as
Variational Inference-Model Predictive Control, Model Predictive PathIntegral
Control, Cross Entropy Method, and Stein VariationalInference Model Predictive
Control as special cases. The proposed algorithm allows for effective control
of the cost/reward transform and is characterized by superior performance in
terms of mean and variance reduction of the associated cost. The aforementioned
features are supported by a theoretical and numerical analysis on the level of
risk sensitivity of the proposed algorithm as well as simulation experiments on
5 different robotic systems with 3 different policy parameterizations.
