Generalized Model Predictive Path Integral Control as Expectation–Maximization
Year: 2026
Type: article
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.
Source: IEEE Control Systems Letters
Authors: Jiarui Wang, Sina Sharifi, Mahyar Fazlyab
Institution: Johns Hopkins University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,645
OpenAlex ID: W7166801246