NDLI: Online learning for stochastic linear optimization problems

Content Provider	IEEE Xplore Digital Library
Author	Keqin Liu Qing Zhao
Copyright Year	2012
Description	Author affiliation: Department of Electrical and Computer Engineering, University of California, Davis, 95616, USA (Keqin Liu; Qing Zhao)
Abstract	We consider the stochastic online linear optimization problems under unknown cost models. At each time, an action is chosen from a compact subset in $R^{d}$ and a random cost with an unknown distribution (depending on the action) is incurred. The expected value of the random cost is assumed to be a (unknown) linear function over the action space. The objective is to minimize the growth rate of regret (i.e., the increase in expected total cost compared to the ideal scenario with known cost models) in terms of both problem size and time horizon length. We propose a policy that achieves a regret polynomial in the problem size and sublinear in time. This policy also allows a performance tradeoff in terms of the problem size and the time horizon length: it can offer a linear regret order in problem size with an arbitrarily small sacrifice in the regret order with time. We further consider a special class of the problem when the action space is a polytope or finite and show that a regret logarithmic with time and polynomial with the problem size can be achieved. This special class includes the adaptive shortest-path routing problem in networks with unknown and stochastically varying link sates.
Starting Page	363
Ending Page	367
File Size	117026
Page Count	5
File Format	PDF
ISBN	9781467314732
e-ISBN	9781467314725
DOI	10.1109/ITA.2012.6181775
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-02-05
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stochastic processes Routing Cost function Vectors Polynomials Random variables
Content Type	Text
Resource Type	Article

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