IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v46y2021i1p204-220.html
   My bibliography  Save this article

Efficient Online Linear Optimization with Approximation Algorithms

Author

Listed:
  • Dan Garber

    (Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 3200003, Israel)

Abstract

We revisit the problem of online linear optimization in the case where the set of feasible actions is accessible through an approximated linear optimization oracle with a factor α multiplicative approximation guarantee. This setting in particular is interesting because it captures natural online extensions of well-studied offline linear optimization problems that are NP-hard yet admit efficient approximation algorithms. The goal here is to minimize the α -regret , which is the natural extension to this setting of the standard regret in online learning . We present new algorithms with significantly improved oracle complexity for both the full-information and bandit variants of the problem. Mainly, for both variants, we present α-regret bounds of O ( T − 1 / 3 ) , were T is the number of prediction rounds, using only O ( l o g T ) calls to the approximation oracle per iteration, on average. These are the first results to obtain both the average oracle complexity of O ( l o g T ) (or even polylogarithmic in T ) and α -regret bound O ( T − c ) for a constant c > 0 for both variants.

Suggested Citation

  • Dan Garber, 2021. "Efficient Online Linear Optimization with Approximation Algorithms," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 204-220, February.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:1:p:204-220
    DOI: 10.1287/moor.2020.1053
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/moor.2020.1053
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2020.1053?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rad Niazadeh & Negin Golrezaei & Joshua Wang & Fransisca Susan & Ashwinkumar Badanidiyuru, 2023. "Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization," Management Science, INFORMS, vol. 69(7), pages 3797-3817, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Davidov, Sreten & Pantoš, Miloš, 2017. "Planning of electric vehicle infrastructure based on charging reliability and quality of service," Energy, Elsevier, vol. 118(C), pages 1156-1167.
    2. Filipe Rodrigues & Agostinho Agra & Lars Magnus Hvattum & Cristina Requejo, 2021. "Weighted proximity search," Journal of Heuristics, Springer, vol. 27(3), pages 459-496, June.
    3. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    4. Song, Zhe & Kusiak, Andrew, 2010. "Mining Pareto-optimal modules for delayed product differentiation," European Journal of Operational Research, Elsevier, vol. 201(1), pages 123-128, February.
    5. Seona Lee & Sang-Ho Lee & HyungJune Lee, 2020. "Timely directional data delivery to multiple destinations through relay population control in vehicular ad hoc network," International Journal of Distributed Sensor Networks, , vol. 16(5), pages 15501477209, May.
    6. Zhuang, Yanling & Zhou, Yun & Yuan, Yufei & Hu, Xiangpei & Hassini, Elkafi, 2022. "Order picking optimization with rack-moving mobile robots and multiple workstations," European Journal of Operational Research, Elsevier, vol. 300(2), pages 527-544.
    7. Menghong Li & Yingli Ran & Zhao Zhang, 2022. "A primal-dual algorithm for the minimum power partial cover problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1913-1923, October.
    8. Wang, Yiyuan & Pan, Shiwei & Al-Shihabi, Sameh & Zhou, Junping & Yang, Nan & Yin, Minghao, 2021. "An improved configuration checking-based algorithm for the unicost set covering problem," European Journal of Operational Research, Elsevier, vol. 294(2), pages 476-491.
    9. C Guéret & N Jussien & O Lhomme & C Pavageau & C Prins, 2003. "Loading aircraft for military operations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 458-465, May.
    10. Keisuke Murakami, 2018. "Iterative Column Generation Algorithm for Generalized Multi-Vehicle Covering Tour Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-22, August.
    11. R. L. Francis & T. J. Lowe & Arie Tamir, 2000. "Aggregation Error Bounds for a Class of Location Models," Operations Research, INFORMS, vol. 48(2), pages 294-307, April.
    12. Dongyue Liang & Zhao Zhang & Xianliang Liu & Wei Wang & Yaolin Jiang, 2016. "Approximation algorithms for minimum weight partial connected set cover problem," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 696-712, February.
    13. Abdullah Alshehri & Mahmoud Owais & Jayadev Gyani & Mishal H. Aljarbou & Saleh Alsulamy, 2023. "Residual Neural Networks for Origin–Destination Trip Matrix Estimation from Traffic Sensor Information," Sustainability, MDPI, vol. 15(13), pages 1-21, June.
    14. June Sung Park & Jinyoung Jang & Eunjung Lee, 0. "Theoretical and empirical studies on essence-based adaptive software engineering," Information Technology and Management, Springer, vol. 0, pages 1-13.
    15. Wedelin, Dag, 1995. "The design of a 0-1 integer optimizer and its application in the Carmen system," European Journal of Operational Research, Elsevier, vol. 87(3), pages 722-730, December.
    16. Sun, Yi-Fan & Sun, Zheng-Yang, 2019. "Target observation of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 233-245.
    17. Victor Reyes & Ignacio Araya, 2021. "A GRASP-based scheme for the set covering problem," Operational Research, Springer, vol. 21(4), pages 2391-2408, December.
    18. Taoqing Zhou & Zhipeng Lü & Yang Wang & Junwen Ding & Bo Peng, 2016. "Multi-start iterated tabu search for the minimum weight vertex cover problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 368-384, August.
    19. Giovanni Felici & Sokol Ndreca & Aldo Procacci & Benedetto Scoppola, 2016. "A-priori upper bounds for the set covering problem," Annals of Operations Research, Springer, vol. 238(1), pages 229-241, March.
    20. Owais, Mahmoud & Moussa, Ghada S. & Hussain, Khaled F., 2019. "Sensor location model for O/D estimation: Multi-criteria meta-heuristics approach," Operations Research Perspectives, Elsevier, vol. 6(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormoor:v:46:y:2021:i:1:p:204-220. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.