Online Stochastic Packing and Combinatorial Allocation with General Correlations

[2508.13458] Online Stochastic Packing and Combinatorial Allocation with General Correlations Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2508.13458 (math) [Submitted on 19 Aug 2025 ( v1 ), last revised 26 Aug 2026 (this version, v3)] Title: Online Stochastic Packing and Combinatorial Allocation with General Correlations Authors: Sabri Cetin , Yilun Chen , David A. Goldberg View PDF HTML (experimental) Abstract: There has been a growing interest in studying online stochastic packing and combinatorial allocation under more general correlation structures, motivated by the complex data sets and models driving modern applications. Several past works either assume correlations are weak or have a particular structure, have a complexity scaling with the number of Markovian ``states of the world" (which may be exponentially large in the case of full history dependence), scale poorly with the horizon $T$, or make additional continuity assumptions. We show that for all $\epsilon$, the online stochastic packing (combinatorial allocation) linear programming problem with general correlations (suitably normalized and with sparse columns) has an approximately optimal policy (with optimality gap $\epsilon T$) whose per-decision runtime scales as the time to simulate a single sample path of the underlying stochastic process (assuming access to a Monte Carlo simulator), multiplied by a constant independent of the horizon or number of Markovian states. We derive analogous results for network revenue management (also with flexible products), and online bipartite matching and independent set in bounded-degree graphs, by rounding. Our algorithms implement stochastic gradient methods in a novel on-the-fly/recursive manner for the associated massive deterministic-equivalent linear program. Subjects: Optimization and Control (math.OC) ; Data Structures and Algorithms (cs.DS); Probability (math.PR) Cite as: arXiv:2508.13458 [math.OC] (or arXiv:2508.13458v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2508.13458 Focus to learn more arXiv-issued DOI via DataCite Submission history From: David Goldberg [ view email ] [v1] Tue, 19 Aug 2025 02:32:39 UTC (71 KB) [v2] Sat, 30 Aug 2025 17:46:51 UTC (72 KB) [v3] Wed, 26 Aug 2026 18:00:30 UTC (85 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-08 Change to browse by: cs cs.DS math math.PR References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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