2 Search Results for "Moulin, Serge"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.98
The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization

Authors: Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the online allocation of divisible items to n agents with additive valuations for p-mean welfare maximization, a problem introduced by Barman, Khan, and Maiti (2022). Our algorithmic and hardness results characterize the optimal competitive ratios for the entire spectrum of -∞ ≤ p ≤ 1. Surprisingly, our improved algorithms for all p ≤ (1)/(log n) are simply the greedy algorithm for the Nash welfare, supplemented with two auxiliary components to ensure all agents have non-zero utilities and to help a small number of agents with low utilities. In this sense, the long arm of Nashian allocation achieves near-optimal competitive ratios not only for Nash welfare but also all the way to egalitarian welfare.
Cite as

Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang. The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.ICALP.2025.98,
  author =	{Huang, Zhiyi and Lee, Chui Shan and Shu, Xinkai and Wang, Zhaozi},
  title =	{{The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{98:1--98:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.98},
  URN =		{urn:nbn:de:0030-drops-234754},
  doi =		{10.4230/LIPIcs.ICALP.2025.98},
  annote =	{Keywords: Online Algorithms, Fair Division, Nash Welfare}
}
Document
DOI: 10.4230/LIPIcs.WABI.2018.17
l1-Penalised Ordinal Polytomous Regression Estimators with Application to Gene Expression Studies

Authors: Stéphane Chrétien, Christophe Guyeux, and Serge Moulin

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
Qualitative but ordered random variables, such as severity of a pathology, are of paramount importance in biostatistics and medicine. Understanding the conditional distribution of such qualitative variables as a function of other explanatory variables can be performed using a specific regression model known as ordinal polytomous regression. Variable selection in the ordinal polytomous regression model is a computationally difficult combinatorial optimisation problem which is however crucial when practitioners need to understand which covariates are physically related to the output and which covariates are not. One easy way to circumvent the computational hardness of variable selection is to introduce a penalised maximum likelihood estimator based on some well chosen non-smooth penalisation function such as, e.g., the l_1-norm. In the case of the Gaussian linear model, the l_1-penalised least-squares estimator, also known as LASSO estimator, has attracted a lot of attention in the last decade, both from the theoretical and algorithmic viewpoints. However, even in the Gaussian linear model, accurate calibration of the relaxation parameter, i.e., the relative weight of the penalisation term in the estimation cost function is still considered a difficult problem that has to be addressed with caution. In the present paper, we apply l_1-penalisation to the ordinal polytomous regression model and compare several hyper-parameter calibration strategies. Our main contributions are: (a) a useful and simple l_1 penalised estimator for ordinal polytomous regression and a thorough description of how to apply Nesterov's accelerated gradient and the online Frank-Wolfe methods to the problem of computing this estimator, (b) a new hyper-parameter calibration method for the proposed model, based on the QUT idea of Giacobino et al. and (c) a code which can be freely used that implements the proposed estimation procedure.
Cite as

Stéphane Chrétien, Christophe Guyeux, and Serge Moulin. l1-Penalised Ordinal Polytomous Regression Estimators with Application to Gene Expression Studies. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chretien_et_al:LIPIcs.WABI.2018.17,
  author =	{Chr\'{e}tien, St\'{e}phane and Guyeux, Christophe and Moulin, Serge},
  title =	{{l1-Penalised Ordinal Polytomous Regression Estimators with Application to Gene Expression Studies}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{17:1--17:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.17},
  URN =		{urn:nbn:de:0030-drops-93199},
  doi =		{10.4230/LIPIcs.WABI.2018.17},
  annote =	{Keywords: LASSO, ordinal polytomous regression, Quantile Universal Threshold, Frank-Wolfe algorithm, Nesterov algorithm}
}
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