Variational Inference MPC using Tsallis Divergence

Ziyi O Wang (Georgia Tech),
Oswin So (Georgia Tech),
Jason Gibson (Georgia Tech),
Bogdan Vlahov (Georgia Tech),
Manan Gandhi (Georgia Tech),
Guan-Horng Liu (Georgia Tech),
Evangelos Theodorou (Georgia Tech)
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Paper #073
Interactive Poster Session I Interactive Poster Session IV

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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.

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