Convergence rates of a discrete feedback control arising in mean-field linear quadratic optimal control problems

TL;DR

This paper introduces a discretization method for mean-field linear quadratic control problems using Riccati equations, providing convergence rates and an effective algorithm validated by numerical examples.

Contribution

It presents a novel feedback control-based discretization approach for mean-field LQ problems with proven convergence rates and an efficient computational algorithm.

Findings

Proved convergence rates for the discretization method.

Developed an effective algorithm for solving mean-field LQ problems.

Validated theoretical results with numerical experiments.

Abstract

In this work, we propose a feedback control based temporal discretization for linear quadratic optimal control problems (LQ problems) governed by controlled mean-field stochastic differential equations. We firstly decompose the original problem into two problems: a stochastic LQ problem and a deterministic one. Secondly, we discretize both LQ problems one after another relying on Riccati equations and control's feedback representations. Then, we prove the convergence rates for the proposed discretization and present an effective algorithm. Finally, a numerical example is provided to support the theoretical finding.