Shortest Paths without a Map, but with an Entropic Regularizer

Sebastien Bubeck; Christian Coester; Yuval Rabani

doi:10.1109/FOCS54457.2022.00036

Shortest Paths without a Map, but with an Entropic Regularizer

Sebastien Bubeck, Christian Coester, Yuval Rabani

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In a 1989 paper titled 'shortest paths without a map', Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed by the searcher. This problem, later called layered graph traversal, is parametrized by the maximum cardinality k of a layer of the input graph. It is an online setting for dynamic programming, and it is known to be a rather general and fundamental model of online computing, which includes as special cases other acclaimed models. The deterministic competitive ratio for this problem was soon discovered to be exponential in k, and it is now nearly resolved: it lies between O(2k) and O(k2k). Regarding the randomized competitive ratio, in 1993 Ramesh proved, surprisingly, that this ratio has to be at least O(k2/log1+?k) (for any constant ? > 0). In the same paper, Ramesh also gave an O(k13)-competitive randomized online algorithm. Since 1993, no progress has been reported on the randomized competitive ratio of layered graph traversal. In this work we show how to apply the mirror descent framework on a carefully selected evolving metric space, and obtain an O(k2) competitive randomized online algorithm, nearly matching the known lower bound on the randomized competitive ratio.

Original language	American English
Title of host publication	Proceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022
Publisher	IEEE Computer Society
Pages	1102-1113
Number of pages	12
ISBN (Electronic)	9781665455190
DOIs	https://doi.org/10.1109/FOCS54457.2022.00036
State	Published - 2022
Event	63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022 - Denver, United States Duration: 31 Oct 2022 → 3 Nov 2022

Publication series

Name	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume	2022-October
ISSN (Print)	0272-5428

Conference

Conference	63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022
Country/Territory	United States
City	Denver
Period	31/10/22 → 3/11/22

Bibliographical note

Funding Information:
The second author s research was done while he was at Tel Aviv University, supported by the Israel Academy of Sciences and Humanities and Council for Higher Education Excellence Fellowship Program for International Postdoctoral Researchers. The third author s research was supported in part by ISF grants 3565-21 and 389-22, and by BSF grant 2018687

Funding Information:
The second author’s research was done while he was at Tel Aviv University, supported by the Israel Academy of Sciences and Humanities & Council for Higher Education Excellence Fellowship Program for International Postdoctoral Researchers. The third author’s research was supported in part by ISF grants 3565-21 and 389-22, and by BSF grant 2018687.

Publisher Copyright:
© 2022 IEEE.

Keywords

competitive analysis
online computing
shortest path

Access to Document

10.1109/FOCS54457.2022.00036

Cite this

Bubeck, S., Coester, C., & Rabani, Y. (2022). Shortest Paths without a Map, but with an Entropic Regularizer. In Proceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022 (pp. 1102-1113). (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2022-October). IEEE Computer Society. https://doi.org/10.1109/FOCS54457.2022.00036

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abstract = "In a 1989 paper titled 'shortest paths without a map', Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed by the searcher. This problem, later called layered graph traversal, is parametrized by the maximum cardinality k of a layer of the input graph. It is an online setting for dynamic programming, and it is known to be a rather general and fundamental model of online computing, which includes as special cases other acclaimed models. The deterministic competitive ratio for this problem was soon discovered to be exponential in k, and it is now nearly resolved: it lies between O(2k) and O(k2k). Regarding the randomized competitive ratio, in 1993 Ramesh proved, surprisingly, that this ratio has to be at least O(k2/log1+?k) (for any constant ? > 0). In the same paper, Ramesh also gave an O(k13)-competitive randomized online algorithm. Since 1993, no progress has been reported on the randomized competitive ratio of layered graph traversal. In this work we show how to apply the mirror descent framework on a carefully selected evolving metric space, and obtain an O(k2) competitive randomized online algorithm, nearly matching the known lower bound on the randomized competitive ratio.",

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author = "Sebastien Bubeck and Christian Coester and Yuval Rabani",

note = "Funding Information: The second author s research was done while he was at Tel Aviv University, supported by the Israel Academy of Sciences and Humanities and Council for Higher Education Excellence Fellowship Program for International Postdoctoral Researchers. The third author s research was supported in part by ISF grants 3565-21 and 389-22, and by BSF grant 2018687 Funding Information: The second author{\textquoteright}s research was done while he was at Tel Aviv University, supported by the Israel Academy of Sciences and Humanities & Council for Higher Education Excellence Fellowship Program for International Postdoctoral Researchers. The third author{\textquoteright}s research was supported in part by ISF grants 3565-21 and 389-22, and by BSF grant 2018687. Publisher Copyright: {\textcopyright} 2022 IEEE.; 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022 ; Conference date: 31-10-2022 Through 03-11-2022",

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Bubeck, S, Coester, C & Rabani, Y 2022, Shortest Paths without a Map, but with an Entropic Regularizer. in Proceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022. Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 2022-October, IEEE Computer Society, pp. 1102-1113, 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, Denver, United States, 31/10/22. https://doi.org/10.1109/FOCS54457.2022.00036

Shortest Paths without a Map, but with an Entropic Regularizer. / Bubeck, Sebastien; Coester, Christian; Rabani, Yuval.
Proceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022. IEEE Computer Society, 2022. p. 1102-1113 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2022-October).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Shortest Paths without a Map, but with an Entropic Regularizer

Abstract

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Bibliographical note

Keywords

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