{
  "abstract": "This paper studies projection-free algorithms for stochastic constrained multi-level compositional optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex. Since projection onto the constraint set can be computationally expensive, we develop projection-free methods that rely on linear minimization oracles. For non-convex objectives, we propose variance-reduced projection-free algorithms and establish complexity guarantees under both the Frank-Wolfe gap and the gradient mapping criteria. We also develop momentum-based methods that achieve convergence guarantees under weaker smoothness assumptions. Additionally, by using a stage-wise design, we derive a parameter-free variant that preserves the same complexities for the Frank-Wolfe gap. Such a design can be further used to develop algorithms for convex and strongly convex functions whose rates match those of single-level projection-free counterparts. Finally, we consider finite-sum problems and derive complexities for non-convex, convex, and strongly convex objectives. Numerical experiments across multiple tasks demonstrate the effectiveness of the proposed methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15679",
  "author_total": 7,
  "authors": [
    {
      "name": "Wei Jiang"
    },
    {
      "name": "Sifan Yang"
    },
    {
      "name": "Wenhao Yang"
    },
    {
      "name": "Yibo Wang"
    },
    {
      "name": "Yuanyu Wan"
    },
    {
      "name": "Zechao Li"
    },
    {
      "name": "Lijun Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3g2darvbx1asa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15679",
  "fulltext_url": null,
  "id": "3g2darvbx1asa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15679",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7213353299",
  "pdf_url": "https://arxiv.org/pdf/2609.15679",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3g2darvbx1asa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15679",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15679"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Projection-Free Multi-level Algorithms for Stochastic Constrained Compositional Optimization",
  "title_text": "Projection-Free Multi-level Algorithms for Stochastic Constrained Compositional Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/3g2darvbx1asa",
  "venue": "arXiv",
  "versions": []
}