{
  "abstract": "Predict-then-optimize methods learn a mapping from features to unknown edge costs. They then solve the shortest-path problem on the predicted costs. We study a feature-free alternative for the case where the decision-maker observes many noisy cost vectors on a fixed network. The cost vectors are denoised by an eigenvalue decomposition (PCA) of their covariance matrix. Dijkstra's algorithm then runs on the result. We test this on the $5\\times5$ grid of \\citet{elmachtoub2022}, with $1000$ independent replications and a fresh ground truth in each. We compare against SPO+, against naive Dijkstra on noisy costs, and against two alternatives to a hand-picked rank $k$ (the Gavish-Donoho threshold and a Ledoit-Wolf filter). We also test a hybrid of SPO+ and PCA. Four findings emerge. First, the rank matters. Keeping $k=2$ components performs worse than no denoising. Second, when costs are close to linear in the features, the Gavish-Donoho threshold recovers the true rank without supervision. PCA-denoised Dijkstra outperforms SPO+ at $°=1$, but underperforms SPO+ at $°\\geq 2$. The hybrid works best at $°=1$ and is slightly better than SPO+ at $°=2$. Third, when costs are strongly nonlinear ($°=4$), the signal is no longer low-rank, and only the Ledoit-Wolf filter clearly beats the naive baseline. Fourth, the benefit of denoising grows with network size on grids, but not on a layered non-grid network at high nonlinearity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15111",
  "author_total": 2,
  "authors": [
    {
      "name": "Henry Aldridge-Krawciw"
    },
    {
      "name": "Irene Aldridge"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0kzws4tcthg5s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15111",
  "fulltext_url": null,
  "id": "0kzws4tcthg5s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15111",
  "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",
      "econ.EM"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7213326967",
  "pdf_url": "https://arxiv.org/pdf/2609.15111",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0kzws4tcthg5s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.15111",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15111"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Eigenvalue-Decomposition Cost Denoising for Predict-then-Optimize",
  "title_text": "Eigenvalue-Decomposition Cost Denoising for Predict-then-Optimize",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0kzws4tcthg5s",
  "venue": "arXiv",
  "versions": []
}