{
  "abstract": "We consider stochastic multi-objective optimization over a nonempty closed convex set, where every objective is an expectation and only sample-gradient information is available. We develop a line-search-free and function-value-free adaptive projected-gradient algorithm for the sample-average approximation (SAA) problem. Each iteration computes a feasible regularized multi-gradient step and updates the regularization parameter from the projected step length. A normal-cone-based certificate yields descent estimates and an explicit complexity bound for the Pareto-stationarity residual of the SAA problem. The consistency of SAA gradients then transfers vanishing SAA residuals to Pareto stationarity for the population problem, while an additional concentration argument gives a finite-sample residual bound on compact sets. Experiments on synthetic problems, classification, portfolio selection, multi-task learning, and robot control illustrate the practical performance of our algorithm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02722",
  "author_total": 3,
  "authors": [
    {
      "name": "Yiyang Li"
    },
    {
      "name": "Lei Wang"
    },
    {
      "name": "Xiaojun Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77sbbj4xrxxh4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02722",
  "fulltext_url": null,
  "id": "77sbbj4xrxxh4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02722",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Advanced Multi-Objective Optimization Algorithms"
    ]
  ],
  "openalex": "W7207876433",
  "pdf_url": "https://arxiv.org/pdf/2609.02722",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77sbbj4xrxxh4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02722",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02722"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "An Adaptive Projected-Gradient Algorithm for Sample-Average Approximations of Stochastic Multi-Objective Optimization",
  "title_text": "An Adaptive Projected-Gradient Algorithm for Sample-Average Approximations of Stochastic Multi-Objective Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/77sbbj4xrxxh4",
  "venue": "arXiv",
  "versions": []
}