# Stein Variational Model Predictive Control

arXiv: https://arxiv.org/abs/2011.07641 · HTML: https://mlsanity.com/paper/2011.07641/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2020.

## Built on by (most cited first, 30 of 30)

- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Probabilistic Inference of Simulation Parameters via Parallel Differentiable Simulation](https://mlsanity.com/paper/2109.08815/) (2021)
- [Composable Energy Policies for Reactive Motion Generation and Reinforcement Learning](https://mlsanity.com/paper/2105.04962/) (2021)
- [Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent](https://mlsanity.com/paper/2409.08469/) (2024)
- [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022)
- [Variational Inference MPC using Tsallis Divergence](https://mlsanity.com/paper/2104.00241/) (2021)
- [Dual Online Stein Variational Inference for Control and Dynamics](https://mlsanity.com/paper/2103.12890/) (2021)
- [Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processes](https://mlsanity.com/paper/2210.03512/) (2022)
- [Learning Sampling Distributions for Model Predictive Control](https://mlsanity.com/paper/2212.02587/) (2022)
- [Hierarchical Policy Blending as Inference for Reactive Robot Control](https://mlsanity.com/paper/2210.07890/) (2022)
- [Constrained Stein Variational Trajectory Optimization](https://mlsanity.com/paper/2308.12110/) (2023)
- [Deep Model Predictive Optimization](https://mlsanity.com/paper/2310.04590/) (2023)
- [STAMP: Differentiable Task and Motion Planning via Stein Variational Gradient Descent](https://mlsanity.com/paper/2310.01775/) (2023)
- [Wasserstein Gradient Boosting: A Framework for Distribution-Valued Supervised Learning](https://mlsanity.com/paper/2405.09536/) (2024)
- [Efficient Stochastic Optimal Control through Approximate Bayesian Input Inference](https://mlsanity.com/paper/2105.07693/) (2021)
- [Path Signatures for Diversity in Probabilistic Trajectory Optimisation](https://mlsanity.com/paper/2308.04071/) (2023)
- [Risk-sensitive control as inference with R'enyi divergence](https://mlsanity.com/paper/2411.01827/) (2024)
- [DiSProD: Differentiable Symbolic Propagation of Distributions for Planning](https://mlsanity.com/paper/2302.01491/) (2023)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Global Tensor Motion Planning](https://mlsanity.com/paper/2411.19393/) (2024)
- [Optimisation of Structured Neural Controller Based on Continuous-Time Policy Gradient](https://mlsanity.com/paper/2201.06262/) (2022)
- [Decision-Making Among Bounded Rational Agents](https://mlsanity.com/paper/2210.08672/) (2022)
- [Safe and Efficient Path Planning under Uncertainty via Deep Collision Probability Fields](https://mlsanity.com/paper/2409.04306/) (2024)
- [Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions](https://mlsanity.com/paper/2502.15006/) (2025)
- [A Taxonomy of Self-Handover](https://mlsanity.com/paper/2504.04939/) (2025)
- [Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification](https://mlsanity.com/paper/2506.00589/) (2025)
- [Q-Guided Stein Variational Model Predictive Control via RL-informed Policy Prior](https://mlsanity.com/paper/2507.06625/) (2025)
- [Test-time reward-guided alignment of language models by importance sampling on pre-logit space](https://mlsanity.com/paper/2510.26219/) (2025)
- [BayesFP: Posterior Estimation for Flow-Based Policies via Feynman-Kac Sampling](https://mlsanity.com/paper/2606.21014/) (2026)
- [P3: Persistent Particle Planning for Constrained Diffusion Control](https://mlsanity.com/paper/2610.06002/) (2026)

## Abstract (arXiv)

Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex probability distributions. In this paper, we propose a generalization of MPC that represents a multitude of solutions as posterior distributions. By casting MPC as a Bayesian inference problem, we employ variational methods for posterior computation, naturally encoding the complexity and multi-modality of the decision making problem. We present a Stein variational gradient descent method to estimate the posterior directly over control parameters, given a cost function and observed state trajectories. We show that this framework leads to successful planning in challenging, non-convex optimal control problems.