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Dynamic Regret in Online Convex Optimization with Indicator Switching Costs — arXiv:2609.30556

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.30556
License (as archived): CC0-1.0
Archived: 2026-10-08T02:10:26.366Z
SHA-256 of the archived text: eb6f8af463e96b43d52642900370fa0e41ee773dcbaa98d8ef89f82b46f53f8a
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How to cite

Dynamic Regret in Online Convex Optimization with Indicator Switching Costs — arXiv:2609.30556 — arXiv (en), https://arxiv.org/abs/2609.30556 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_74cff201ec40 (Metraipolis archive dc_74cff201ec40, sha256 eb6f8af463e96b43d52642900370fa0e41ee773dcbaa98d8ef89f82b46f53f8a)

BibTeX

@misc{dc74cff201ec40,
  title = {Dynamic Regret in Online Convex Optimization with Indicator Switching Costs — arXiv:2609.30556},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.30556},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_74cff201ec40; sha256 eb6f8af463e96b43d52642900370fa0e41ee773dcbaa98d8ef89f82b46f53f8a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.30556. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study dynamic regret in online convex optimization with an \emph{indicator switching cost}: a fixed penalty incurred whenever two consecutive decisions differ. This captures startup overheads such as server activation, model deployment, and cache updates, and on a bounded domain it recovers norm-based movement costs as a special case. Existing guarantees for indicator costs handle only static comparators. We show that a direct extension of these techniques to dynamic regret provably fails, motivating a different approach. We propose a meta-learning framework: a set of randomized lazy FTRL base learners restarted at dyadic time scales, aggregated by a movement-aware master that mixes their proposal densities and samples actions via maximal coupling of consecutive mixtures. The resulting algorithm satisfies, in expectation, $\mathcal{R}^{\mathbf{1}}_T \le \tilde{\mathcal{O}}(\min\{\sqrt{T(S_T{+}1)},T^{2/3}(P_T+1)^{1/3}\})$, where $\mathcal{R}^{\mathbf{1}}_T$ is the dynamic regret plus the cumulative indicator switching cost, $S_T$ counts comparator switches, and $P_T$ is the comparator path length. The bound holds simultaneously for all sequences and requires no prior knowledge of $S_T$ or $P_T$: it is minimax-optimal (up to logarithmic factors) for tracking piecewise-constant comparators, and also captures frequently moving comparators with small total path length.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-28 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.30556 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T01:43:06.678Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).