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Competitively chasing convex bodies

Authors:

Sébastien Bubeck,

Yin Tat Lee,

Yuanzhi Li,

Mark SellkeAuthors Info & Claims

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

Pages 861 - 868

https://doi.org/10.1145/3313276.3316314

Published: 23 June 2019 Publication History

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Abstract

Let F be a family of sets in some metric space. In the F-chasing problem, an online algorithm observes a request sequence of sets in F and responds (online) by giving a sequence of points in these sets. The movement cost is the distance between consecutive such points. The competitive ratio is the worst case ratio (over request sequences) between the total movement of the online algorithm and the smallest movement one could have achieved by knowing in advance the request sequence. The family F is said to be chaseable if there exists an online algorithm with finite competitive ratio. In 1991, Linial and Friedman conjectured that the family of convex sets in Euclidean space is chaseable. We prove this conjecture.

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Cited By

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Cohen LSharifi-Malvajerdi SStangl KVakilian AZiani JKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Sequential strategic screeningProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3618658(6279-6295)Online publication date: 23-Jul-2023
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Index Terms

Competitively chasing convex bodies
1. Theory of computation
  1. Design and analysis of algorithms
    1. Online algorithms

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In the chasing convex bodies problem, an online player receives a request sequence of N convex sets K₁,..., K_N contained in a normed space R^d. The player starts at [MATH HERE], and after observing each K_n picks a new point [MATH HERE]. At each step the ...

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Published In

STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing

June 2019

1258 pages

ISBN:9781450367059

DOI:10.1145/3313276

General Chair:
Moses Charikar
Stanford University
,
Program Chair:
Edith Cohen
Google, USA / Tel Aviv University, Israel

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 23 June 2019

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National Science Foundation

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STOC '19

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SIGACT

STOC '19: 51st Annual ACM SIGACT Symposium on the Theory of Computing

June 23 - 26, 2019

AZ, Phoenix, USA

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

View all

De MJain SKallepalli SSingh S(2024)Online Geometric Covering and PiercingAlgorithmica10.1007/s00453-024-01244-186:9(2739-2765)Online publication date: 3-Jun-2024
https://doi.org/10.1007/s00453-024-01244-1
Cohen LSharifi-Malvajerdi SStangl KVakilian AZiani JKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Sequential strategic screeningProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3618658(6279-6295)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3618658
Guan YPan LShishika DTsiotras P(2023)On the Adversarial Convex Body Chasing Problem2023 American Control Conference (ACC)10.23919/ACC55779.2023.10156405(435-440)Online publication date: 31-May-2023
https://doi.org/10.23919/ACC55779.2023.10156405
Ding R(2023)Stochastic Dominance, Risk, and Weak Sub-majorization with Applications to Portfolio OptimizationProceedings of the 2023 6th International Conference on Mathematics and Statistics10.1145/3613347.3613357(63-71)Online publication date: 14-Jul-2023
https://dl.acm.org/doi/10.1145/3613347.3613357
Argue CGupta AMolinaro M(2023)Lipschitz Selectors May Not Yield Competitive Algorithms for Convex Body ChasingDiscrete & Computational Geometry10.1007/s00454-023-00491-3Online publication date: 5-Jul-2023
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Sellke M(2023)Chasing Convex Bodies OptimallyGeometric Aspects of Functional Analysis10.1007/978-3-031-26300-2_12(313-335)Online publication date: 30-Sep-2023
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Ramesh SSessa PKrause ABogunovic IKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Movement penalized Bayesian optimization with application to wind energy systemsProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602230(27036-27048)Online publication date: 28-Nov-2022
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Zhang LJiang WYi JYang TKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Smoothed online convex optimization based on discounted-normal-predictorProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3600626(4928-4942)Online publication date: 28-Nov-2022
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Pan WShi GLin YWierman A(2022)Online Optimization with Feedback Delay and Nonlinear Switching CostProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/35080376:1(1-34)Online publication date: 28-Feb-2022
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