Discrete-Time Maximum Likelihood Neural Distribution Steering

TL;DR

This paper introduces a neural network-based method for steering the distribution of discrete-time dynamical systems from an initial to a target distribution within finite time, extending continuous-time techniques to discrete settings.

Contribution

It presents a novel regularized maximum likelihood optimization framework for distribution steering in discrete-time systems using neural networks, including solutions for complex, non-Gaussian, and nonlinear cases.

Findings

Successfully applied to benchmark problems with semidefinite programming solutions.

Extended to complex problems with non-Gaussian boundary conditions.

Demonstrated effectiveness on nonlinear discrete-time systems.

Abstract

This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control policies, parametrized by neural networks. Although similar solutions have been explored in the continuous-time context, extending these techniques to systems with discrete dynamics is not trivial. The proposed algorithm results in a regularized maximum likelihood optimization problem, which is solved using machine learning techniques. After presenting the algorithm, we provide several numerical examples that illustrate the capabilities of the proposed method. We start from a simple problem that admits a solution through semidefinite programming, serving as a benchmark for the proposed approach. Then, we employ the framework in more general problems that cannot be solved using existing techniques, such as problems with non-Gaussian boundary distributions and non-linear dynamics.