Generalized Model Predictive Path Integral Control as Expectation--Maximization
Abstract
Model Predictive Path Integral (MPPI) control is a powerful sampling-based method for solving stochastic optimal control problems and has enabled real-time control in complex robotic systems. Despite its empirical success, its theoretical understanding remains limited. In this work, we show that MPPI can be interpreted as a special case of the Expectation-Maximization (EM) algorithm applied to a probabilistic inference formulation of optimal control. This perspective leads to a generalized EM-MPPI framework that extends MPPI beyond the commonly used Gaussian parameterization. We analyze the convergence behavior of this algorithm and characterize the local convergence rate in terms of the covariance of the posterior trajectory distribution and the exploration distribution. For exponential-family distributions, we establish a sufficient increase property of the log-likelihood when the log-partition function is strongly convex. Specializing the analysis to Gaussian MPPI yields explicit global and local convergence characterizations. The code for the experiments will be available upon acceptance.
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BibTeX
@misc{wang2026generalized,
title = {{Generalized Model Predictive Path Integral Control as Expectation--Maximization}},
author = {Jiarui Wang and Sina Sharifi and Mahyar Fazlyab},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.00317},
eprint = {2606.00317},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.00317},
}
RIS
TY - UNPB
TI - Generalized Model Predictive Path Integral Control as Expectation--Maximization
AU - Jiarui Wang
AU - Sina Sharifi
AU - Mahyar Fazlyab
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2606.00317
UR - https://arxiv.org/abs/2606.00317
AB - Model Predictive Path Integral (MPPI) control is a powerful sampling-based method for solving stochastic optimal control problems and has enabled real-time control in complex robotic systems. Despite its empirical success, its theoretical understanding remains limited. In this work, we show that MPPI can be interpreted as a special case of the Expectation-Maximization (EM) algorithm applied to a probabilistic inference formulation of optimal control. This perspective leads to a generalized EM-MPPI framework that extends MPPI beyond the commonly used Gaussian parameterization. We analyze the convergence behavior of this algorithm and characterize the local convergence rate in terms of the covariance of the posterior trajectory distribution and the exploration distribution. For exponential-family distributions, we establish a sufficient increase property of the log-likelihood when the log-partition function is strongly convex. Specializing the analysis to Gaussian MPPI yields explicit global and local convergence characterizations. The code for the experiments will be available upon acceptance.
ER -