{
  "abstract": "We propose NB-HalpernSGD via LM-MultiLRSGA, a two-phase optimizer for multi-objective optimization. The process starts with a competitive optimization phase by applying a limited-memory variant of MultiLRSGA, named LM-MultiLRSGA, designed to reduce the memory footprint of the original optimizer while preserving its rotational correction mechanism. It addresses multi-objective tasks by considering the competitive game associated with the original multi-objective problem, approximating a Nash equilibrium. This point defines a Nash-equilibrium-induced disagreement point: we formulate the Nash bargaining problem associated with the original losses and rewrite its Nash product as a logarithmic minimization surrogate. This minimization problem is solved using HalpernSGD, anchored at the computed competitive reference point. Therefore, the method uses the Nash equilibrium as a principled reference point for the bargaining stage and then moves toward a Pareto-oriented solution of the original multi-objective problem. We validate the proposed optimizer on a PINN-inspired neural model, where it outperforms established multi-objective optimizers, including PCGrad, MultiAdam, and DualConeGD. Finally, while the convergence properties of HalpernSGD have been extensively studied, we discuss the convergence and stability properties of the proposed LM-MultiLRSGA phase.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03616",
  "author_total": 3,
  "authors": [
    {
      "name": "Katherine Rossella Foglia"
    },
    {
      "name": "Francesco Sergio Pisani"
    },
    {
      "name": "Vittorio Colao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ajqavsytac8y2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03616",
  "fulltext_url": null,
  "id": "ajqavsytac8y2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03616",
  "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": "W7208730280",
  "pdf_url": "https://arxiv.org/pdf/2609.03616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ajqavsytac8y2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Nash-Bargaining HalpernSGD via Limited-Memory MultiLRSGA: A Two-Phase Optimizer for Multi-Objective Learning",
  "title_text": "Nash-Bargaining HalpernSGD via Limited-Memory MultiLRSGA: A Two-Phase Optimizer for Multi-Objective Learning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/ajqavsytac8y2",
  "venue": "arXiv",
  "versions": []
}