# Constrained Stein Variational Trajectory Optimization

arXiv: https://arxiv.org/abs/2308.12110 · HTML: https://mlsanity.com/paper/2308.12110/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 75 references that are in the map.
- First posted on arXiv 23 Aug 2023.

## Builds on (most cited first, 30 of 33)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Sample-efficient Cross-Entropy Method for Real-time Planning](https://mlsanity.com/paper/2008.06389/) (2020)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [STORM: An Integrated Framework for Fast Joint-Space Model-Predictive Control for Reactive Manipulation](https://mlsanity.com/paper/2104.13542/) (2021)
- [Variational Inference MPC for Bayesian Model-based Reinforcement Learning](https://mlsanity.com/paper/1907.04202/) (2019)
- [Stein Variational Gradient Descent With Matrix-Valued Kernels](https://mlsanity.com/paper/1910.12794/) (2019)
- [Stein Variational Model Predictive Control](https://mlsanity.com/paper/2011.07641/) (2020)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Asymptotically Optimal Sampling-based Kinodynamic Planning](https://mlsanity.com/paper/1407.2896/) (2014)
- [Stochastic Optimal Control as Approximate Input Inference](https://mlsanity.com/paper/1910.03003/) (2019)
- [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022)
- [Multimodal Trajectory Optimization for Motion Planning](https://mlsanity.com/paper/2003.07054/) (2020)
- [Variational Inference MPC using Tsallis Divergence](https://mlsanity.com/paper/2104.00241/) (2021)
- [Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descent](https://mlsanity.com/paper/2210.06447/) (2022)
- [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)
- [GuSTO: Guaranteed Sequential Trajectory Optimization via Sequential Convex Programming](https://mlsanity.com/paper/1903.00155/) (2019)
- [A Gaussian variational inference approach to motion planning](https://mlsanity.com/paper/2209.05655/) (2022)
- [Probabilistic Framework for Constrained Manipulations and Task and Motion Planning under Uncertainty](https://mlsanity.com/paper/2003.04259/) (2020)
- [Entropy Regularized Motion Planning via Stein Variational Inference](https://mlsanity.com/paper/2107.05146/) (2021)
- [Robust & Asymptotically Locally Optimal UAV-Trajectory Generation Based on Spline Subdivision](https://mlsanity.com/paper/2010.09904/) (2020)
- [Constrained Covariance Steering Based Tube-MPPI](https://mlsanity.com/paper/2110.07744/) (2021)

## Built on by (most cited first, 8 of 8)

- [Deep Model Predictive Optimization](https://mlsanity.com/paper/2310.04590/) (2023)
- [Diffusion-Informed Probabilistic Contact Search for Multi-Finger Manipulation](https://mlsanity.com/paper/2410.00841/) (2024)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Diffusing Trajectory Optimization Problems for Recovery During Multi-Finger Manipulation](https://mlsanity.com/paper/2510.07030/) (2025)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Manifold Sampling via Entropy Maximization](https://mlsanity.com/paper/2605.12338/) (2026)
- [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)

## Abstract (arXiv)

We present Constrained Stein Variational Trajectory Optimization (CSVTO), an algorithm for performing trajectory optimization with constraints on a set of trajectories in parallel. We frame constrained trajectory optimization as a novel form of constrained functional minimization over trajectory distributions, which avoids treating the constraints as a penalty in the objective and allows us to generate diverse sets of constraint-satisfying trajectories. Our method uses Stein Variational Gradient Descent (SVGD) to find a set of particles that approximates a distribution over low-cost trajectories while obeying constraints. CSVTO is applicable to problems with differentiable equality and inequality constraints and includes a novel particle re-sampling step to escape local minima. By explicitly generating diverse sets of trajectories, CSVTO is better able to avoid poor local minima and is more robust to initialization. We demonstrate that CSVTO outperforms baselines in challenging highly-constrained tasks, such as a 7DoF wrench manipulation task, where CSVTO outperforms all baselines both in success and constraint satisfaction.