Variational Inference MPC using Tsallis Divergence

In this paper; we provide a generalized framework for Variational Inference-Stochastic Optimal Control by using the non-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 Path Integral Control; Cross Entropy Method; and Stein Variational Inference 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.