Consistency of tug-of-war type operators on random data clouds

2025/07/24 by Jeongmin Han, Han, Jeongmin, Huajie Liu +1
Computer Science · #Analysis of PDEs (math.AP) #Anomaly Detection Techniques and Applications #FOS: Mathematics #Network Security and Intrusion Detection #Neural Networks and Applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2507.18383

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a tug-of-war type operator on geometric graphs and its associated Dirichlet problem on a random data cloud. Specifically, we analyze the convergence of the value functions as the number of data points increases and the step size of the game shrinks. This analysis reveals the connection between our tug-of-war type operator and the corresponding model problem. A key ingredient in establishing this result is the consistency of the operator.

Citations

• Krylov-Safonov theory for Pucci-type extremal inequalities on random data clouds
• Notes on tug-of-war games and the p-Laplace equation
• Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth
• Asymptotic Mean-Value Formulas for Solutions of General Second-Order Elliptic Equations
• Time-dependent tug-of-war games and normalized parabolic p-Laplace equations
• Lipschitz regularity of graph Laplacians on random data clouds
• A Course on Tug-of-War Games with Random Noise
• The game theoretic p-Laplacian and semi-supervised learning with few labels
• Local regularity for time-dependent tug-of-war games with varying\n probabilities
• Tug of war with noise: a game theoretic view of the p-Laplacian
• Reinforcement Learning: An Introduction

Related

• Krylov-Safonov theory for Pucci-type extremal inequalities on random data clouds
• Random Tug of War games for the \mathbf p-Laplacian: \mathbf1
• Totalitarian random Tug-of-War games in graphs
• Gradient and Lipschitz estimates for tug-of-war type games
• A Course on Tug-of-War Games with Random Noise