Error Analysis of Sampling Algorithms for Approximating Stochastic Optimal Control

Publication Links

• DOI    • arXiV    • Abstract    • Citation

Abstract

This paper is concerned with the error analysis of two types of sampling algorithms, namely model predictive path integral (MPPI) and an interacting particle system (IPS) algorithm, that have been proposed in the literature for numerical approximation of the stochastic optimal control. The analysis is presented through the lens of Gibbs variational principle. For an illustrative example of a single-stage stochastic optimal control problem, analytical expressions for approximation error and scaling laws, with respect to the state dimension and sample size, are derived. The analytical results are illustrated with numerical simulations.

Citation

@misc{joshi2025erroranalysissamplingalgorithms,
      title={Error Analysis of Sampling Algorithms for Approximating Stochastic Optimal Control}, 
      author={Anant A. Joshi and Amirhossein Taghvaei and Prashant G. Mehta},
      year={2025},
      eprint={2504.02198},
      archivePrefix={arXiv},
      primaryClass={eess.SY},
      url={https://arxiv.org/abs/2504.02198}, 
abstract = {This paper is concerned with the error analysis of two types of sampling
 algorithms, namely model predictive path integral (MPPI) and an 
interacting particle system (IPS) algorithm, that have been proposed in
 the literature for numerical approximation of the stochastic optimal 
control. The analysis is presented through the lens of Gibbs variational
 principle. For an illustrative example of a single-stage stochastic 
optimal control problem, analytical expressions for approximation error 
and scaling laws, with respect to the state dimension and sample size, 
are derived. The analytical results are illustrated with numerical 
simulations.
    }
}