A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems

[2506.09776] A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2506.09776 (math) [Submitted on 11 Jun 2025 ( v1 ), last revised 10 Apr 2026 (this version, v3)] Title: A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems Authors: Shabnam Khodakaramzadeh , Soroosh Shafiee , Gabriel de Albuquerque Gleizer , Peyman Mohajerin Esfahani View a PDF of the paper titled A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems, by Shabnam Khodakaramzadeh and 3 other authors View PDF HTML (experimental) Abstract: We study the factor model problem, which aims to uncover low-dimensional structures in high-dimensional datasets. Adopting a robust data-driven approach, we formulate the problem as a saddle-point optimization. Our primary contribution is a first-order algorithm that solves this reformulation by leveraging a linear minimization oracle (LMO). We further develop semi-closed form solutions (up to a scalar) for three specific LMOs, corresponding to the Frobenius norm, Kullback-Leibler divergence, and Gelbrich (aka Wasserstein) distance. The analysis includes explicit quantification of these LMOs' regularity conditions, notably the Lipschitz constants of the dual function, which govern the algorithm's convergence performance. Numerical experiments confirm our method's effectiveness in high-dimensional settings, outperforming standard off-the-shelf optimization solvers. Subjects: Optimization and Control (math.OC) ; Systems and Control (eess.SY) Cite as: arXiv:2506.09776 [math.OC] (or arXiv:2506.09776v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2506.09776 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shabnam Khodakaramzadeh [ view email ] [v1] Wed, 11 Jun 2025 14:13:32 UTC (262 KB) [v2] Mon, 9 Feb 2026 09:32:31 UTC (284 KB) [v3] Fri, 10 Apr 2026 11:00:57 UTC (286 KB) Full-text links: Access Paper: View a PDF of the paper titled A Saddle Point Algorithm for Robust Data-Driven Factor Model Problems, by Shabnam Khodakaramzadeh and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-06 Change to browse by: cs cs.SY eess eess.SY math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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