# Efficient Stochastic Optimal Control through Approximate Bayesian Input Inference

arXiv: https://arxiv.org/abs/2105.07693 · HTML: https://mlsanity.com/paper/2105.07693/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 102 references that are in the map.
- First posted on arXiv 17 May 2021.

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

- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Probabilistic Numerics and Uncertainty in Computations](https://mlsanity.com/paper/1506.01326/) (2015)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [Variational Bayesian Reinforcement Learning with Regret Bounds](https://mlsanity.com/paper/1807.09647/) (2018)
- [An Online Learning Approach to Model Predictive Control](https://mlsanity.com/paper/1902.08967/) (2019)
- [Stein Variational Model Predictive Control](https://mlsanity.com/paper/2011.07641/) (2020)
- [Adaptive importance sampling for control and inference](https://mlsanity.com/paper/1505.01874/) (2015)
- [Optimal steering of a linear stochastic system to a final probability distribution](https://mlsanity.com/paper/1408.2222/) (2014)
- [From self-tuning regulators to reinforcement learning and back again](https://mlsanity.com/paper/1906.11392/) (2019)
- [Stochastic Optimal Control as Approximate Input Inference](https://mlsanity.com/paper/1910.03003/) (2019)
- [Dual Control for Approximate Bayesian Reinforcement Learning](https://mlsanity.com/paper/1510.03591/) (2015)
- [Nonlinear Covariance Control via Differential Dynamic Programming](https://mlsanity.com/paper/1911.09283/) (2019)
- [Finite-Horizon Covariance Control of Linear Time-Varying Systems](https://mlsanity.com/paper/1707.04729/) (2017)
- [Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform](https://mlsanity.com/paper/2003.03679/) (2020)
- [Advancing Trajectory Optimization with Approximate Inference: Exploration, Covariance Control and Adaptive Risk](https://mlsanity.com/paper/2103.06319/) (2021)
- [Risk Sensitive, Nonlinear Optimal Control: Iterative Linear Exponential-Quadratic Optimal Control with Gaussian Noise](https://mlsanity.com/paper/1512.07173/) (2015)
- [Approximately Optimal Continuous-Time Motion Planning and Control via Probabilistic Inference](https://mlsanity.com/paper/1702.07335/) (2017)
- [On Approximate Nonlinear Gaussian Message Passing On Factor Graphs](https://mlsanity.com/paper/1903.09136/) (2019)
- [Direct Policy Optimization using Deterministic Sampling and Collocation](https://mlsanity.com/paper/2010.08506/) (2020)

## Built on by (most cited first, 3 of 3)

- [Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processes](https://mlsanity.com/paper/2210.03512/) (2022)
- [Deterministic Trajectory Optimization through Probabilistic Optimal Control](https://mlsanity.com/paper/2407.13316/) (2024)
- [Structured Cooperative Multi-Agent Reinforcement Learning: a Bayesian Network Perspective](https://mlsanity.com/paper/2510.09937/) (2025)

## Abstract (arXiv)

Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate inference techniques can be used to handle the statistical approximations principled and practically by framing the control problem as a problem of input estimation. Analyzing the Gaussian setting, we present an inference-based solver that is effective in stochastic and deterministic settings and was found to be superior to popular baselines on nonlinear simulated tasks. We draw connections that relate this inference formulation to previous approaches for stochastic optimal control and outline several advantages that this inference view brings due to its statistical nature.