{
  "abstract": "Continual learning (CL) aims to learn from sequential tasks while mitigating catastrophic forgetting when historical data are no longer accessible. We study continual learning for high-dimensional sparse linear regression, where $\\ell_1$ regularization creates a difficulty absent from continual ridge regression: that recursively reusing an $\\ell_1$-penalized estimator can propagate earlier shrinkage and accumulate regularization bias across tasks. We propose score-preserving continual Lasso (SP-CL), which separates sparse estimation from state transmission by preserving the historical squared-loss score. Under squared loss, its cumulative estimator exactly recovers a full-history Lasso minimizer. When task coefficients coincide, it inherits the full-history sparse rate. For related task-specific coefficients, SP-CL uses a regularized current-task correction that leaves the transmitted state unchanged and attains the offline source-assisted rate under an oracle related-task condition. We also derive Overall/BWT/FWT decompositions that distinguish historical information loss, task conflict, and current-task specialization, and validate the resulting regimes in simulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32708",
  "author_total": 3,
  "authors": [
    {
      "name": "Jingyi Guo"
    },
    {
      "name": "Runze Li"
    },
    {
      "name": "Lingzhou Xue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58w6jkhsg3fmy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32708",
  "fulltext_url": null,
  "id": "58w6jkhsg3fmy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32708",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7223673253",
  "pdf_url": "https://arxiv.org/pdf/2610.32708",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58w6jkhsg3fmy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32708",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32708"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Score-Preserving Continual Lasso under Task Shift",
  "title_text": "Score-Preserving Continual Lasso under Task Shift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:25Z",
  "url": "https://research.draconitic.com/paper/58w6jkhsg3fmy",
  "venue": "arXiv",
  "versions": []
}