TY - GEN

T1 - Learning with global cost in stochastic environments

AU - Even-Dar, Eyal

AU - Mannor, Shie

AU - Mansour, Yishay

PY - 2010

Y1 - 2010

N2 - We consider an online learning setting where at each time step the decision maker has to choose how to distribute the future loss between k alternatives, and then observes the loss of each alternative, where the losses are assumed to come from a joint distribution. Motivated by load balancing and job scheduling, we consider a global cost function (over the losses incurred by each alternative), rather than a summation of the instantaneous losses as done traditionally in online learning. Specifically, we consider the global cost functions: (1) the makespan (the maximum over the alternatives) and (2) the Ld norm (over the alternatives) for d > 1. We design algorithms that guarantee logarithmic regret for this setting, where the regret is measured with respect to the best static decision (one selects the same distribution over alternatives at every time step). We also show that the least loaded machine, a natural algorithm for minimizing the makespan, has a regret of the order of √T. We complement our theoretical findings with supporting experimental results.

AB - We consider an online learning setting where at each time step the decision maker has to choose how to distribute the future loss between k alternatives, and then observes the loss of each alternative, where the losses are assumed to come from a joint distribution. Motivated by load balancing and job scheduling, we consider a global cost function (over the losses incurred by each alternative), rather than a summation of the instantaneous losses as done traditionally in online learning. Specifically, we consider the global cost functions: (1) the makespan (the maximum over the alternatives) and (2) the Ld norm (over the alternatives) for d > 1. We design algorithms that guarantee logarithmic regret for this setting, where the regret is measured with respect to the best static decision (one selects the same distribution over alternatives at every time step). We also show that the least loaded machine, a natural algorithm for minimizing the makespan, has a regret of the order of √T. We complement our theoretical findings with supporting experimental results.

UR - http://www.scopus.com/inward/record.url?scp=84898073088&partnerID=8YFLogxK

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AN - SCOPUS:84898073088

SN - 9780982252925

T3 - COLT 2010 - The 23rd Conference on Learning Theory

SP - 80

EP - 92

BT - COLT 2010 - The 23rd Conference on Learning Theory

T2 - 23rd Conference on Learning Theory, COLT 2010

Y2 - 27 June 2010 through 29 June 2010

ER -