TY - GEN

T1 - Online linear optimization over permutations

AU - Yasutake, Shota

AU - Hatano, Kohei

AU - Kijima, Shuji

AU - Takimoto, Eiji

AU - Takeda, Masayuki

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - This paper proposes an algorithm for online linear optimization problem over permutations; the objective of the online algorithm is to find a permutation of {1,...,n} at each trial so as to minimize the "regret" for T trials. The regret of our algorithm is O(n 2√T ln n) in expectation for any input sequence. A naive implementation requires more than exponential time. On the other hand, our algorithm uses only O(n) space and runs in O(n 2) time in each trial. To achieve this complexity, we devise two efficient algorithms as subroutines: One is for minimization of an entropy function over the permutahedron P n , and the other is for randomized rounding over P n .

AB - This paper proposes an algorithm for online linear optimization problem over permutations; the objective of the online algorithm is to find a permutation of {1,...,n} at each trial so as to minimize the "regret" for T trials. The regret of our algorithm is O(n 2√T ln n) in expectation for any input sequence. A naive implementation requires more than exponential time. On the other hand, our algorithm uses only O(n) space and runs in O(n 2) time in each trial. To achieve this complexity, we devise two efficient algorithms as subroutines: One is for minimization of an entropy function over the permutahedron P n , and the other is for randomized rounding over P n .

UR - http://www.scopus.com/inward/record.url?scp=84055193634&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84055193634&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-25591-5_55

DO - 10.1007/978-3-642-25591-5_55

M3 - Conference contribution

AN - SCOPUS:84055193634

SN - 9783642255908

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 534

EP - 543

BT - Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings

T2 - 22nd International Symposium on Algorithms and Computation, ISAAC 2011

Y2 - 5 December 2011 through 8 December 2011

ER -