Application-Driven Development of Computational Tools and Algorithms for Machine Learning and Mean-Field Games - Research and Development

Aug 4, 2026

A dissertation on building computational tools and algorithms for optimization, machine learning, and mean-field games. It introduces MFGLib, an open-source Python library for solving Nash equilibria in generic mean-field games. It reformulates Nash-equilibrium search as non-convex optimization, then proposes occupation-time-adapted perturbations—PGDOT and PAGDOT—to escape saddle points with theoretical guarantees and numerical evidence. It also develops a stacking ensemble for detecting ophthalmology overutilization and healthcare fraud in Medicare.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages111

Reading Time4 h 40 min

AccessFree to download

Introduction

MFGLib: A Library for Mean-Field Games

Related Work

Brief Overview of MFGLib

Future Work

Escaping Saddle Points Efficiently with Occupation-Time-Adapted Perturbations

Background and Existing Results

Main Results

Empirical Results

Conclusion

Leveraging Stacked Generalization to Effectively Detect Overutilization in Medicare

Data Source, Preprocessing, and Labeling

Overutilization Analysis via Machine Learning Techniques

Discussion

Limitations

UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Application-Driven Development of Computational Tools and Algorithms for Machine Learning and Mean-Field Games Permalink [https://escholarship.org/uc/item/8b39r1m1](https://escholarship.org/uc/item/8b39r1m1) Author Tajrobehkar, Mahan Publication Date 2023 Peer reviewed|Thesis/dissertation [eScholarship.org](eScholarship.org) Powered by the California Digital Library University of California Application-Driven Development of Computational Tools and Algorithms for Machine Learning and Mean-Field Games By Mahan Tajrobehkar A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering-Industrial Engineering and Operations Research in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Xin Guo, Chair Professor Zeyu Zheng Professor Anant Sahai Summer 2023 Application-Driven Development of Computational Tools and Algorithms for Machine Learning and Mean-Field Games Copyright 2023 by Mahan Tajrobehkar 1 Abstract Application-Driven Development of Computational Tools and Algorithms for Machine Learning and Mean-Field Games by Mahan Tajrobehkar Doctor of Philosophy in Engineering-Industrial Engineering and Operations Research University of California, Berkeley Professor Xin Guo, Chair In today’s rapidly evolving technological landscape, the development and advancement of computational tools and algorithms have become paramount across a wide range of research fields. This holds particularly true in various domains of computational mathematics, encompassing areas such as machine learning, optimization, and algorithmic game theory. The computational tools serve as essential enablers, empowering researchers and practitioners by facilitating efficient modeling, analysis, and prediction. Algorithms are essential components of computational tools, which provide instructions for data processing, pattern recognition, and decision-making. This dissertation focuses on developing computational tools and algorithms for specific applications in the interconnected fields of optimization, machine learning (ML), and meanfield games (MFGs) . First, to address the absence of a comprehensive computational tool for MFGs, we present MFGLib, an open-source Python library designed to provide a userfriendly and customizable interface for solving Nash equilibria in generic MFGs. Second, we demonstrate that the search for Nash equilibria in MFGs and various ML problems can be formulated as non-convex optimization problems, where the presence of saddle points significantly impedes the effectiveness of gradient descent algorithm and its variants. To help optimization algorithms escape saddle points efficiently, we introduce a novel perturbation mechanism based on the dynamics of vertex-repelling random walk. This leads to the development of two new algorithms, perturbed gradient descent adapted to occupation time (PGDOT) and its accelerated version (PAGDOT) . Theoretical guarantees for these algorithms are established, and through extensive numerical experiments, we showcase their superiority over several state-of-the-art optimization methods. Last, we explore a relatively independent machine learning task—detecting overutilization and fraud in healthcare. We focus on developing an ensemble model based on Stacked Generalization (stacking) to detect overutilization in Medicare within the field of Ophthalmology. Our results highlight 2 the superiority of the stacking ensemble model over traditional ML models in accurately distinguishing overutilizing ophthalmologists from non-fraudulent ones. i To my parents, for ensuring every educational opportunity was available to me. ii Contents Contents ii List of Figures iv List of Tables vii 1 Introduction 1 1. 1 Related Publications . . . . . . .

FAQs

What is MFGLib and what problem does it address?

MFGLib is an open-source Python library for solving Nash equilibria in generic mean-field games, designed to provide a user-friendly and customizable interface.

How are Nash equilibrium searches in mean-field games connected to optimization?

They are reformulated as non-convex optimization problems, where saddle points hinder the effectiveness of gradient descent variants.

What do PGDOT and PAGDOT contribute to optimization?

They introduce a perturbation mechanism based on vertex-repelling random walk dynamics, with theoretical guarantees and numerical experiments showing improved performance over state-of-the-art optimization methods.

Aug 4, 2026

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