{
  "abstract": "Stochastic dual dynamic programming (SDDP) and its variants are run in practice with forward passes that sample the noise at random. Recent iteration-complexity results favour another choice: when the trial points are selected deterministically, for instance along the scenario with the largest gap, the number of iterations is polynomial in the horizon $T$, whereas every bound we know of for randomly sampled forward passes is exponential in $T$. We show that this is not intrinsic to random sampling, for a broad class of trajectory-following dynamic programming algorithms, which includes SDDP, stochastic dual dynamic integer programming and stochastic Lipschitz dynamic programming. With random sampling, and with Lipschitz constants, diameters and per-stage loss ranges bounded independently of the stage and of the horizon, the expected number of iterations whose policy is not $T\\varepsilon$-optimal is $O(T\\varepsilon^{-(d+1)})$, where $d$ is the state dimension: linear in $T$, as for deterministic selection rules. The proof needs no particular scenario to be sampled: the gap between the expected cost of the current policy and the current lower bound equals the expected sum of one-step Bellman residuals along the sampled path, and Lipschitz cuts that are tight at the visited states turn the positive residuals into permanent increases of a bounded potential. The results extend to noise without finite support, to backward passes on a sample average approximation, and to stationary and periodic infinite-horizon SDDP with geometric pass lengths.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12713",
  "author_total": 1,
  "authors": [
    {
      "name": "Vincent Leclere"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bacxyvzkhrj56.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12713",
  "fulltext_url": null,
  "id": "bacxyvzkhrj56",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12713",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7221513929",
  "pdf_url": "https://arxiv.org/pdf/2610.12713",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bacxyvzkhrj56.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12713",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12713"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "SDDP has polynomial iteration complexity in the horizon",
  "title_text": "SDDP has polynomial iteration complexity in the horizon",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/bacxyvzkhrj56",
  "venue": "arXiv",
  "versions": []
}