{
  "abstract": "Policy gradients for autoregressive sequence models differentiate each token's log-probability while holding the conditioning history fixed. This discards information about how earlier decisions shape later conditional distributions, creating a credit-assignment bottleneck when rewards are sparse. We introduce History-Reparameterized (HR) policy gradients, which replace the frozen prefix in the score function with a differentiable reparameterized or relaxed history, allowing gradients of downstream log-probabilities to propagate backward through the generated trajectory. The resulting history-pathwise term is generally biased when added directly, so we derive Optimal HR (OHR), a centered control-variate estimator with a closed-form coefficient that minimizes the trace of the gradient variance at the population level. The variance reduction is governed by temporal structure in the policy dynamics: random or weakly structured policies provide little benefit, while policies with learned sequential dependencies yield informative history-pathwise corrections. For discrete tokens, the choice of relaxation is crucial: embedding-level relaxation yields substantial variance reduction that grows with horizon, whereas straight-through Gumbel-Softmax yields essentially none in our diagnostics. We validate the method on a Gaussian linear Markov model, a sparse-reward T-maze with a recurrent policy, and an autoregressive Transformer model for small Traveling Salesman Problem (TSP) instances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24188",
  "author_total": 5,
  "authors": [
    {
      "name": "Mohammad Hossein Amani"
    },
    {
      "name": "Leonardo Bocchieri"
    },
    {
      "name": "Maxime Peyrard"
    },
    {
      "name": "Clément Hongler"
    },
    {
      "name": "Robert West"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ch47xxxdmrn87.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24188",
  "fulltext_url": null,
  "id": "ch47xxxdmrn87",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24188",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7223046115",
  "pdf_url": "https://arxiv.org/pdf/2610.24188",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ch47xxxdmrn87.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2610.24188",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24188"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "On Reparameterizing the Score Function",
  "title_text": "On Reparameterizing the Score Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/ch47xxxdmrn87",
  "venue": "arXiv",
  "versions": []
}