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Direct Search Methods for Online Nonconvex Optimization Under Inexact Bandit Feedback — arXiv:2608.08979

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.08979
License (as archived): CC0-1.0
Archived: 2026-10-19T09:05:27.945Z
SHA-256 of the archived text: 060eafc2f24ede07b2d69b51c8af9d89d6f17549528b59d441fa1de52135ae61
Stable URL of this page: https://metraipolis.com/documento/dc_39bcfdedf19c

How to cite

Direct Search Methods for Online Nonconvex Optimization Under Inexact Bandit Feedback — arXiv:2608.08979 — arXiv (en), https://arxiv.org/abs/2608.08979 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_39bcfdedf19c (Metraipolis archive dc_39bcfdedf19c, sha256 060eafc2f24ede07b2d69b51c8af9d89d6f17549528b59d441fa1de52135ae61)

BibTeX

@misc{dc39bcfdedf19c,
  title = {Direct Search Methods for Online Nonconvex Optimization Under Inexact Bandit Feedback — arXiv:2608.08979},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.08979},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_39bcfdedf19c; sha256 060eafc2f24ede07b2d69b51c8af9d89d6f17549528b59d441fa1de52135ae61},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.08979. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Optimization under zeroth-order (i.e., bandit) feedback is central to many engineering problems where the analytic forms of objectives and/or constraints are unavailable. In modern applications, such as online control and online learning, optimization problems often evolve with time, requiring adaptive optimization methodologies. Yet, existing methods in this seting are largely confined to adaptations of methodologies developed for time-invariant or first-order optimization, and thus often rely on gradient surrogates that fail to fully exploit the zeroth-order structure of the available information. In this paper, we propose a randomized two-point direct-search algorithm for nonconvex time-varying optimization and derive iteration-complexity bounds under both constant and diminishing probing ratios. The resulting analysis yields explicit stationarity bounds in terms of the temporal variability of the problem and possible oracle errors. Our complexity bounds recover the complexity of existing zeroth-order methods in the time-invariant setting, while extending direct- search methods beyond static settings. As an illustrative application, we show that the methodology is naturally suited to solve optimal (equilibrium-selection) control problems for dynamical systems. In this setting, the analysis yields explicit stationarity bounds in terms of the temporal variability of the problem, measured through the effects of plant dynamics and exogenous disturbance variations.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-11 in math.OC).
Categorie arXiv: Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2608.08979 — 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 2026-10-19T09:03:32.068Z dalla pagina https://arxiv.org/catchup/math.OC/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).