{
  "abstract": "Lipschitz bandits admit near-optimal regret $\\widetilde O_d(T^{(d+1)/(d+2)})$ with little memory under full adaptivity, or with few batches under unrestricted memory. We characterize the minimax expected pseudo-regret over $T$ rounds with $W$ bits of memory and at most $B$ batches in dimension $d$. For every memory budget $W$, we prove a lower bound of order $T^{\\frac{d+2}{d+3}} (1+(B-1)W)^{-\\frac{1}{d(d+3)}}$. When $W\\gtrsim_d\\log(eT)$, algorithms with fixed batch boundaries attain, up to logarithmic factors, the larger of this bound and the optimal $B$-batch regret with unrestricted memory. The analysis separates fine-scale comparisons from the regional information needed to allocate their samples at low regret. Attaining $\\widetilde O_d(T^{(d+1)/(d+2)})$ regret requires both $B=Ω_d(\\log\\log T)$ and $(B-1)W=\\widetildeΩ_d(T^{d/(d+2)})$. With one bit of memory, minimax regret is $\\widetildeΘ_d(TB^{-1/(d+2)})$ under adaptive batch boundaries while $Θ_d(T)$ under fixed boundaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07922",
  "author_total": 2,
  "authors": [
    {
      "name": "Zicheng Lyu"
    },
    {
      "name": "Zengfeng Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6j7cvfywbcmn0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07922",
  "fulltext_url": null,
  "id": "6j7cvfywbcmn0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07922",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7202211717",
  "pdf_url": "https://arxiv.org/pdf/2608.07922",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6j7cvfywbcmn0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2608.07922",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07922"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Memory--Batch Tradeoffs in Lipschitz Bandits",
  "title_text": "Memory--Batch Tradeoffs in Lipschitz Bandits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/6j7cvfywbcmn0",
  "venue": "arXiv",
  "versions": []
}