Last-iterate convergence of modified predictive method via high-resolution differential equation on bilinear game

TL;DR

This paper analyzes the convergence of a modified predictive method in bilinear games using high-resolution differential equations, providing theoretical guarantees and addressing gaps in existing literature.

Contribution

It introduces a high-resolution differential equation model for the modified predictive method and proves its convergence in bilinear games, extending prior work.

Findings

Convergence of MPM-HRDE in bilinear games established

Uniqueness of solutions for MPM-HRDE shown

Addresses gaps in existing convergence analysis

Abstract

This paper discusses the convergence of the modified predictive method (MPM) proposed by Liang and stokes corresponding to high-resolution differential equations (HRDE) in bilinear games. First, we present the high-resolution differential equations (MPM-HRDE) corresponding to the MPM. Then, we discuss the uniqueness of the solution for MPM-HRDE in bilinear games. Finally, we provide the convergence results of MPM-HRDE in bilinear games. The results obtained in this paper address the gap in the existing literature and extend the conclusions of related works.