TY - GEN

T1 - Online learning with composite loss functions

AU - Dekel, Ofer

AU - Ding, Jian

AU - Koren, Tomer

AU - Peres, Yuval

N1 - Publisher Copyright:
© 2014 O. Dekel, J. Ding, T. Koren & Y. Peres.

PY - 2014

Y1 - 2014

N2 - We study a new class of online learning problems where each of the online algorithm's actions is assigned an adversarial value, and the loss of the algorithm at each step is a known and deterministic function of the values assigned to its recent actions. This class includes problems where the algorithm's loss is the minimum over the recent adversarial values, the maximum over the recent values, or a linear combination of the recent values. We analyze the minimax regret of this class of problems when the algorithm receives bandit feedback, and prove that when the minimum or maximum functions are used, the minimax regret is Ω(T2/3) (so called hard online learning problems), and when a linear function is used, the minimax regret is Ω(/T) (so called easy learning problems). Previously, the only online learning problem that was known to be provably hard was the multi-armed bandit with switching costs.

AB - We study a new class of online learning problems where each of the online algorithm's actions is assigned an adversarial value, and the loss of the algorithm at each step is a known and deterministic function of the values assigned to its recent actions. This class includes problems where the algorithm's loss is the minimum over the recent adversarial values, the maximum over the recent values, or a linear combination of the recent values. We analyze the minimax regret of this class of problems when the algorithm receives bandit feedback, and prove that when the minimum or maximum functions are used, the minimax regret is Ω(T2/3) (so called hard online learning problems), and when a linear function is used, the minimax regret is Ω(/T) (so called easy learning problems). Previously, the only online learning problem that was known to be provably hard was the multi-armed bandit with switching costs.

UR - http://www.scopus.com/inward/record.url?scp=84939637632&partnerID=8YFLogxK

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AN - SCOPUS:84939637632

T3 - Proceedings of Machine Learning Research

SP - 1214

EP - 1231

BT - Proceedings of The 27th Conference on Learning Theory

A2 - Balcan, Maria Florina

A2 - Feldman, Vitaly

A2 - Szepesvári, Csaba

PB - PMLR

T2 - 27th Conference on Learning Theory, COLT 2014

Y2 - 13 June 2014 through 15 June 2014

ER -