{
  "abstract": "Stochastic compositional optimization minimizes $F(f(x), x)$ over a compact convex set when the inner map $f$ is available only through noisy samples. We propose Hybrid Momentum Stochastic Frank--Wolfe, a projection-free method for outer functions $F$ that are jointly convex and Lipschitz but not necessarily differentiable, such as maxima, CVaR, and norms. The method tracks the Jacobian and the value of $f$ with momentum, using a Taylor correction for the value, and passes the tracked linearization to a generalized linear minimization oracle. Under finite-variance noise, it attains an expected generalized Frank--Wolfe gap of order $K^{-1/4}$ for non-convex objectives and, when the linearized models minorize the objective, a last-iterate primal error of order $K^{-1/3}$. The analysis extends to heavy-tailed noise without clipping, with separate moment orders for values and Jacobians. With an exact oracle, the method reduces to the deterministic method of Vladarean et al. (2023).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15350",
  "author_total": 2,
  "authors": [
    {
      "name": "El Mahdi Chayti"
    },
    {
      "name": "Mohamad Fakhouri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5c4vnnh54gxhf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15350",
  "fulltext_url": null,
  "id": "5c4vnnh54gxhf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15350",
  "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": "W7161601739",
  "pdf_url": "https://arxiv.org/pdf/2605.15350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5c4vnnh54gxhf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2605.15350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe",
  "title_text": "Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/5c4vnnh54gxhf",
  "venue": "arXiv",
  "versions": []
}