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The Curvature of Regret in Contextual Linear Optimization — arXiv:2610.01980

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01980
License (as archived): CC0-1.0
Archived: 2026-10-06T15:34:13.530Z
SHA-256 of the archived text: 8b8919ba49aecc602eeac9910c6af1a42148bf8436c666e31cb4eb32f17a2ddf
Stable URL of this page: https://metraipolis.com/documento/dc_c3ec00a5bdf7

How to cite

The Curvature of Regret in Contextual Linear Optimization — arXiv:2610.01980 — arXiv (en), https://arxiv.org/abs/2610.01980 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c3ec00a5bdf7 (Metraipolis archive dc_c3ec00a5bdf7, sha256 8b8919ba49aecc602eeac9910c6af1a42148bf8436c666e31cb4eb32f17a2ddf)

BibTeX

@misc{dcc3ec00a5bdf7,
  title = {The Curvature of Regret in Contextual Linear Optimization — arXiv:2610.01980},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01980},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c3ec00a5bdf7; sha256 8b8919ba49aecc602eeac9910c6af1a42148bf8436c666e31cb4eb32f17a2ddf},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01980. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Decision-focused learning for linear optimization is complicated by the discontinuity of the optimizer, where small cost errors may leave the decision unchanged or move it to a different vertex. We show that this non-smooth pointwise behavior becomes locally quadratic after averaging over the data distribution, and we derive the curvature in closed form, specifically, a matrix-valued measure supported on the walls of the normal fan. This measure depends only on the feasible set, with the data distribution entering only as a weight. We then offer a tractable approximation for this curvature, computable with just one projection to the feasible set. We prove that the approximation weakly converges to the true population curvature. We offer one application of our findings, a decision-aware scenario generation method for expected-cost linear optimization. Our experiments test the quadratic and weak convergence laws and show a 30.8% regret improvement over uniform allocation on battery arbitrage.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-10-02 in stat.ML).
Categorie arXiv: Machine Learning (cs.LG) ; Optimization and Control (math.OC); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.01980 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T15:12:55.914Z dalla pagina https://arxiv.org/catchup/stat.ML/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).