2 Search Results for "Morgenstern, Jamie"

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.106

Polylogarithmic Approximations for Robust s-t Path

Authors: Shi Li, Chenyang Xu, and Ruilong Zhang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

The paper revisits the Robust s-t Path problem, one of the most fundamental problems in robust optimization. In the problem, we are given a directed graph with n vertices and k distinct cost functions (scenarios) defined over edges, and aim to choose an s-t path such that the total cost of the path is always provable no matter which scenario is realized. Viewing each cost function as an agent, our goal is to find a fair s-t path, which minimizes the maximum cost among all agents. The problem is NP-hard to approximate within a factor of o(log k) unless NP ⊆ DTIME(n^{polylog n}), and the best-known approximation ratio is Õ(√n), which is based on the natural flow linear program. A longstanding open question is whether we can achieve a polylogarithmic approximation for the problem; it remains open even if a quasi-polynomial running time is allowed. Our main result is a O(log n log k) approximation for the Robust s-t Path problem in quasi-polynomial time, solving the open question in the quasi-polynomial time regime. The algorithm is built on a novel linear program formulation for a decision-tree-type structure, which enables us to overcome the Ω(√n) integrality gap for the natural flow LP. Furthermore, we show that for graphs with bounded treewidth, the quasi-polynomial running time can be improved to a polynomial. We hope our techniques can offer new insights into this problem and other related problems in robust optimization.

Cite as

Shi Li, Chenyang Xu, and Ruilong Zhang. Polylogarithmic Approximations for Robust s-t Path. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 106:1-106:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.ICALP.2024.106,
  author =	{Li, Shi and Xu, Chenyang and Zhang, Ruilong},
  title =	{{Polylogarithmic Approximations for Robust s-t Path}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{106:1--106:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.106},
  URN =		{urn:nbn:de:0030-drops-202497},
  doi =		{10.4230/LIPIcs.ICALP.2024.106},
  annote =	{Keywords: Approximation Algorithm, Randomized LP Rounding, Robust s-t Path}
}

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DOI: 10.4230/LIPIcs.FORC.2023.10

Distributionally Robust Data Join

Authors: Pranjal Awasthi, Christopher Jung, and Jamie Morgenstern

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Abstract

Suppose we are given two datasets: a labeled dataset and unlabeled dataset which also has additional auxiliary features not present in the first dataset. What is the most principled way to use these datasets together to construct a predictor? The answer should depend upon whether these datasets are generated by the same or different distributions over their mutual feature sets, and how similar the test distribution will be to either of those distributions. In many applications, the two datasets will likely follow different distributions, but both may be close to the test distribution. We introduce the problem of building a predictor which minimizes the maximum loss over all probability distributions over the original features, auxiliary features, and binary labels, whose Wasserstein distance is r₁ away from the empirical distribution over the labeled dataset and r₂ away from that of the unlabeled dataset. This can be thought of as a generalization of distributionally robust optimization (DRO), which allows for two data sources, one of which is unlabeled and may contain auxiliary features.

Cite as

Pranjal Awasthi, Christopher Jung, and Jamie Morgenstern. Distributionally Robust Data Join. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{awasthi_et_al:LIPIcs.FORC.2023.10,
  author =	{Awasthi, Pranjal and Jung, Christopher and Morgenstern, Jamie},
  title =	{{Distributionally Robust Data Join}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.10},
  URN =		{urn:nbn:de:0030-drops-179311},
  doi =		{10.4230/LIPIcs.FORC.2023.10},
  annote =	{Keywords: Distributionally Robust Optimization, Semi-Supervised Learning, Learning Theory}
}

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