{
  "abstract": "Reinforcement Learning with Verifiable Rewards (RLVR) improves reasoning in language models, but scalar outcomes provide coarse supervision over response trajectories. Self-distillation offers denser token-level guidance by comparing an unassisted policy with a feedback-informed self-teacher, yet the teacher evolves with the student, creating unstable targets and motivating additional regularization. We introduce Function-Space Policy Optimization (FSPO), a single-policy framework that combines current privileged adaptation with function-space temporal consolidation. FSPO stores sparse historical next-token distributions as fixed temporal targets, providing temporal separation without maintaining a persistent teacher model. It further introduces privileged disagreement correction to explicitly suppress locally overvalued actions, reliability-adaptive grounding that strengthens reference supervision when self-generated evidence repeatedly fails, and quality and coverage-aware temporal memory that retains verified behaviors and improves privileged demonstrations. Across reasoning and tool-use benchmarks, FSPO achieves the highest average accuracy under a 5-hour training budget, improving over the strongest baseline by approximately 4% points on average while reducing peak memory from about 70 GB to 56 GB on Olmo3-7B-Instruct.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19687",
  "author_total": 3,
  "authors": [
    {
      "name": "Aryan Das"
    },
    {
      "name": "Arnab Bhattacharya"
    },
    {
      "name": "Vinay Kumar Verma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1znscf748h3gn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19687",
  "fulltext_url": null,
  "id": "1znscf748h3gn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19687",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.CL"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7222075700",
  "pdf_url": "https://arxiv.org/pdf/2610.19687",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1znscf748h3gn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19687",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19687"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Function-Space Temporal Self-Distillation for Policy Optimization",
  "title_text": "Function-Space Temporal Self-Distillation for Policy Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/1znscf748h3gn",
  "venue": "arXiv",
  "versions": []
}