Efficient Online Linear Optimization with Approximation Algorithms

Dan Garber ()
Additional contact information
Dan Garber: Faculty of Industrial Engineering and Management, Technion–Israel Institute of Technology, Haifa 3200003, Israel

Mathematics of Operations Research, 2021, vol. 46, issue 1, 204-220

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.

Keywords: online learning; online linear optimization; regret minimization; approximation algorithms; online algorithms (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://doi.org/10.1287/moor.2020.1053 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:1:p:204-220

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().