{
  "abstract": "Momentum is a classical tool for accelerating convex optimization and a standard component of modern large language model training. Yet recent empirical work has questioned the usefulness of first-moment momentum in reinforcement learning with verifiable rewards (RLVR). We study this question through a bandit formulation of RLVR with bias-corrected exponential moving average (EMA) momentum, where the EMA coefficient $β$ controls how quickly the weights on past gradients decay. When policy gradients are evaluated exactly, we prove that increasing $β$ within a range that prevents overshoot strictly accelerates optimization. When gradients are estimated from sampled responses, a positive expected gain can be obscured by sampling fluctuations. We show that as the learning rate $η$ decreases, the expected gain with fixed $β$ vanishes faster than these fluctuations, whereas increasing $β$ to keep $η/(1-β)$ within the safe regime preserves a nonvanishing gain that eventually dominates them. Bandit simulations quantitatively validate these predictions. RLVR experiments on Qwen3-4B-Base using SGD with EMA and AdamW support our principle of choosing larger coefficients in practical LLM post-training. On Qwen2.5-32B with AdamW, simply increasing $β_1$ improves mean validation accuracy by nearly $2$ percentage points over the conventional choice, demonstrating the principle's effectiveness at a larger model scale.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20413",
  "author_total": 5,
  "authors": [
    {
      "name": "Kaifei Wang"
    },
    {
      "name": "Zikang Shan"
    },
    {
      "name": "Liwei Wang"
    },
    {
      "name": "Yinyu Ye"
    },
    {
      "name": "Han Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5e5bh0jqm0j9j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20413",
  "fulltext_url": null,
  "id": "5e5bh0jqm0j9j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20413",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7222156654",
  "pdf_url": "https://arxiv.org/pdf/2610.20413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5e5bh0jqm0j9j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "When Does Momentum Help in Reinforcement Learning with Verifiable Rewards?",
  "title_text": "When Does Momentum Help in Reinforcement Learning with Verifiable Rewards?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/5e5bh0jqm0j9j",
  "venue": "arXiv",
  "versions": []
}