DocumentCode :
655209
Title :
Playing Non-linear Games with Linear Oracles
Author :
Garber, Dan ; Hazan, Etai
Author_Institution :
Technion - Israel Inst. of Technol., Haifa, Israel
fYear :
2013
fDate :
26-29 Oct. 2013
Firstpage :
420
Lastpage :
428
Abstract :
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and admit significantly less efficient algorithms. This motivates the computational model of online decision making and optimization using a linear optimization oracle. In this computational model we give the first efficient decision making algorithm with optimal regret guarantees, answering an open question of Kalai and Vempala, Hazan and Kale, in case the decision set is a polytope. We also give an extension of the algorithm for the partial information setting, i.e. the "bandit" model. Our method is based on a novel variant of the conditional gradient method, or Frank-Wolfe algorithm, that reduces the task of minimizing a smooth convex function over a domain to that of minimizing a linear objective. Whereas previous variants of this method give rise to approximation algorithms, we give such algorithm that converges exponentially faster and thus runs in polynomial-time for a large class of convex optimization problems over polyhedral sets, a result of independent interest.
Keywords :
combinatorial mathematics; computational complexity; optimisation; Frank-Wolfe algorithm; approximation algorithms; combinatorial algorithms; conditional gradient method; convex optimization problems; linear optimization oracle; matching polytopes; matroid polytopes; online decision making algorithm; path polytopes; smooth convex function; Algorithm design and analysis; Approximation algorithms; Convergence; Convex functions; Games; Gradient methods; Convex Optimization; Online Algorithms; Regret Minimization;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium on
Conference_Location :
Berkeley, CA
ISSN :
0272-5428
Type :
conf
DOI :
10.1109/FOCS.2013.52
Filename :
6686178
Link To Document :
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