{
  "abstract": "Multi-objective bilevel optimization has wide applications in the AI area such as automated learning and multi-task meta-learning. Although recently some works have been begun to study the multi-objective bilevel optimization, the proposed methods rely on the (strongly) convex lower level problems. In fact, these multi-objective bilevel learning problems are generally nonconvex, and particularly their lower level problems are nonconvex. To fill this gap, we propose a class of Multi-Objective Moreau Envelope based Hessian-free Algorithms (MOMEHA) for the multi-objective bilevel learning problems with nonconvex lower level. Specifically, our method uses the Moreau envelope to relax the original problem into a multi-objective single-level optimization with an envelope constraint. In particular, our method retains computational advantages of being single-loop and Hessian-free in the multi-objective setting by incorporating a smooth weighted Tchebycheff scalarization. Furthermore, we propose a momentum-based variant of MOMEHA (i.e., MB-MOMEHA) method for the stochastic multi-objective bilevel learning problems. In theory, we provide the convergence properties of our algorithms under both deterministic and stochastic setting. Some experiments on few-shot meta-learning and neural architecture search demonstrate that our methods outperform the existing approaches in Pareto front, validating its effectiveness and robustness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.12704",
  "author_total": 2,
  "authors": [
    {
      "name": "Yicong Jiang"
    },
    {
      "name": "Feihu Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9ng6kkeqqx3s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.12704",
  "fulltext_url": null,
  "id": "a9ng6kkeqqx3s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.12704",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Advanced Multi-Objective Optimization Algorithms"
    ]
  ],
  "openalex": "W7203451560",
  "pdf_url": "https://arxiv.org/pdf/2608.12704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9ng6kkeqqx3s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.12704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.12704"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level",
  "title_text": "Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/a9ng6kkeqqx3s",
  "venue": "arXiv",
  "versions": []
}