# Variational Inference MPC using Tsallis Divergence

arXiv: https://arxiv.org/abs/2104.00241 · HTML: https://mlsanity.com/paper/2104.00241/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 1 Apr 2021.

## Builds on (most cited first, 19 of 19)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Learning Robot Skills with Temporal Variational Inference](https://mlsanity.com/paper/2006.16232/) (2020)
- [Message Passing Stein Variational Gradient Descent](https://mlsanity.com/paper/1711.04425/) (2017)
- [Variational Inference MPC for Bayesian Model-based Reinforcement Learning](https://mlsanity.com/paper/1907.04202/) (2019)
- [Stein Variational Model Predictive Control](https://mlsanity.com/paper/2011.07641/) (2020)
- [f-Divergence Variational Inference](https://mlsanity.com/paper/2009.13093/) (2020)
- [Variational Inference with Tail-adaptive f-Divergence](https://mlsanity.com/paper/1810.11943/) (2018)
- [FlightGoggles: A Modular Framework for Photorealistic Camera, Exteroceptive Sensor, and Dynamics Simulation](https://mlsanity.com/paper/1905.11377/) (2019)
- [Tsallis Reinforcement Learning: A Unified Framework for Maximum Entropy Reinforcement Learning](https://mlsanity.com/paper/1902.00137/) (2019)
- [Alpha-Beta Divergence For Variational Inference](https://mlsanity.com/paper/1805.01045/) (2018)
- [Non-Smooth Newton Methods for Deformable Multi-Body Dynamics](https://mlsanity.com/paper/1907.04587/) (2019)
- [Gradient-Based Adaptive Stochastic Search for Non-Differentiable Optimization](https://mlsanity.com/paper/1301.1333/) (2013)
- [Constrained Sampling-based Trajectory Optimization using Stochastic Approximation](https://mlsanity.com/paper/1911.04621/) (2019)
- [Information Theoretic Model Predictive Control on Jump Diffusion Processes](https://mlsanity.com/paper/1807.06108/) (2018)
- [Adaptive Risk Sensitive Model Predictive Control with Stochastic Search](https://mlsanity.com/paper/2009.01090/) (2020)

## Built on by (most cited first, 11 of 11)

- [Your Policy Regularizer is Secretly an Adversary](https://mlsanity.com/paper/2203.12592/) (2022)
- [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022)
- [Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processes](https://mlsanity.com/paper/2210.03512/) (2022)
- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)
- [CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design](https://mlsanity.com/paper/2401.07369/) (2024)
- [Generative Predictive Control: Flow Matching Policies for Dynamic and Difficult-to-Demonstrate Tasks](https://mlsanity.com/paper/2502.13406/) (2025)
- [Information-Theoretic Measures on Lattices for High-Order Interactions](https://mlsanity.com/paper/2408.07533/) (2024)
- [Risk-sensitive control as inference with R'enyi divergence](https://mlsanity.com/paper/2411.01827/) (2024)
- [Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions](https://mlsanity.com/paper/2502.15006/) (2025)
- [NashFormer: Leveraging Local Nash Equilibria for Semantically Diverse Trajectory Prediction](https://mlsanity.com/paper/2305.17600/) (2023)
- [Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification](https://mlsanity.com/paper/2506.00589/) (2025)

## Abstract (arXiv)

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.