Metraipolis › archive › dc_2dafa5acea52

Universal Dynamic Portfolios — arXiv:2609.34643

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.34643
License (as archived): CC0-1.0
Archived: 2026-10-07T22:38:32.822Z
SHA-256 of the archived text: a11f86a84801d8faf8104dd71df759ba213e23d4f8d87201ea0a472179beead1
Stable URL of this page: https://metraipolis.com/documento/dc_2dafa5acea52

How to cite

Universal Dynamic Portfolios — arXiv:2609.34643 — arXiv (en), https://arxiv.org/abs/2609.34643 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2dafa5acea52 (Metraipolis archive dc_2dafa5acea52, sha256 a11f86a84801d8faf8104dd71df759ba213e23d4f8d87201ea0a472179beead1)

BibTeX

@misc{dc2dafa5acea52,
  title = {Universal Dynamic Portfolios — arXiv:2609.34643},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.34643},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2dafa5acea52; sha256 a11f86a84801d8faf8104dd71df759ba213e23d4f8d87201ea0a472179beead1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.34643. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Cover's Universal Portfolio (Cover, 1991) matches the performance of the best constant rebalanced portfolio in hindsight. We generalize this framework to compete with an arbitrary comparator sequence $\mathbf{u}_1,\ldots,\mathbf{u}_T$, leading to a dynamic regret minimization problem for the log loss where existing methods break down due to potentially unbounded gradients. The log loss is exp-concave, a curvature property that classically yields fast rates for static regret, yet we show that this advantage generally disappears in the dynamic setting. In particular, a linear-loss-type $\sqrt{TP_T}$ dependence is unavoidable, where $P_T=\sum_{t=2}^T\lVert\mathbf{u}_t-\mathbf{u}_{t-1}\rVert_1$ is the standard path length. This limitation stems from the coarse nature of $P_T$, which obscures finer spatial and temporal structure of the comparator sequence. We therefore introduce two structure-aware measures---the Jensen-Shannon distance for spatial structure and the JS$^q$-path length for temporal structure---under which faster rates are attainable when the comparator sequence has favorable structure. To achieve sharp bounds for both measures simultaneously, we develop Universal Dynamic Portfolio, a parameter-free method that combines a new Dirichlet Hedge algorithm with a fixed-share update, while retaining a near-optimal $P_T$ guarantee in the worst case. Finally, under an additional bounded-gradient assumption, we show that OPS admits the faster $T^{1/3}P_T^{2/3}$ dynamic regret rate over all comparator sequences. We attain this rate with a tractable proper algorithm that applies more broadly to general online exp-concave optimization over arbitrary compact convex domains.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-29 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.34643 — 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 2026-10-07T22:14:28.267Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).