NDLI: Beating the adaptive bandit with high probability

Content Provider	IEEE Xplore Digital Library
Author	Abernethy, J. Rakhlin, A.
Copyright Year	2009
Description	Author affiliation: Department of Statistics, University of Pennsylvania, USA (Rakhlin, A.) \|\| Computer Science Division, UC Berkeley, USA (Abernethy, J.)
Abstract	We provide a principled way of proving Õ(√T) high-probability guarantees for partial-information (bandit) problems over arbitrary convex decision sets. First, we prove a regret guarantee for the full-information problem in terms of “local” norms, both for entropy and self-concordant barrier regularization, unifying these methods. Given one of such algorithms as a black-box, we can convert a bandit problem into a full-information problem using a sampling scheme. The main result states that a high-probability Õ(√T) bound holds whenever the black-box, the sampling scheme, and the estimates of missing information satisfy a number of conditions, which are relatively easy to check. At the heart of the method is a construction of linear upper bounds on confidence intervals. As applications of the main result, we provide the first known efficient algorithm for the sphere with an Õ(√T) high-probability bound. We also derive the result for the n-simplex, improving the O(√nT log(nT)) bound of Auer et al [3] by replacing the log T term with log log T and closing the gap to the lower bound of Ω(√nT). While Õ(√T) high-probability bounds should hold for general decision sets through our main result, construction of linear upper bounds depends on the particular geometry of the set; we believe that the sphere example already exhibits the necessary ingredients. The guarantees we obtain hold for adaptive adversaries (unlike the in-expectation results of [1]) and the algorithms are efficient, given that the linear upper bounds on confidence can be computed.
Starting Page	280
Ending Page	289
File Size	293918
Page Count	10
File Format	PDF
ISBN	9781424439904
DOI	10.1109/ITA.2009.5044958
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-02-08
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Jacobian matrices Computer science Heart Upper bound Probability Cost function Sampling methods Entropy Statistics State estimation
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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