{
  "abstract": "We study strongly adaptive regret for Online Convex Optimization (OCO) with time-varying movement costs, a setting that evaluates a learner's performance over arbitrary sub-intervals. This framework captures complex sequential decision-making problems where both the environment and the cost of switching decisions fluctuate over time. We propose a novel algorithm which, for any interval $[a,b] \\subseteq [T]$, achieves a data-dependent regret bound of $ \\widetilde{\\mathcal{O}}\\left( \\sqrt{(D^2+DP_{[a,b]})\\sum_{t \\in [a,b]}(\\|g_t\\|^2+λ_t\\|g_t\\|)} \\right) $, where $D$ is the diameter of the decision domain, $P_{[a,b]}$ is the path length of the comparator sequence over $[a,b]$, $g_t$ is the gradient of the loss, and $λ_t$ is the movement-cost coefficient at round $t$. Key to our approach is a novel reduction to sleeping experts with movement costs, a previously unexplored variant that is of independent interest. As a result of this development, we further establish the first strongly-adaptive guarantees under delayed feedback. Our approach also naturally extends to OCO with time-varying memory, where we obtain strongly-adaptive guarantees which improve the best-known bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32740",
  "author_total": 4,
  "authors": [
    {
      "name": "Andrew Jacobsen"
    },
    {
      "name": "Emmanuel Esposito"
    },
    {
      "name": "Hao Qiu"
    },
    {
      "name": "Mengxiao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58ng67y3nzae4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32740",
  "fulltext_url": null,
  "id": "58ng67y3nzae4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32740",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7223671030",
  "pdf_url": "https://arxiv.org/pdf/2610.32740",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58ng67y3nzae4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:25Z",
      "native_id": "2610.32740",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32740"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Strongly Adaptive Online Learning with Time-Varying Movement Costs",
  "title_text": "Strongly Adaptive Online Learning with Time-Varying Movement Costs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:25Z",
  "url": "https://research.draconitic.com/paper/58ng67y3nzae4",
  "venue": "arXiv",
  "versions": []
}