Learning with global cost in stochastic environments

Eyal Even-Dar, Shie Mannor, Yishay Mansour

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationCOLT 2010 - The 23rd Conference on Learning Theory
Pages80-92
Number of pages13
StatePublished - 2010
Event23rd Conference on Learning Theory, COLT 2010 - Haifa, Israel
Duration: 27 Jun 201029 Jun 2010

Publication series

NameCOLT 2010 - The 23rd Conference on Learning Theory

Conference

Conference23rd Conference on Learning Theory, COLT 2010
Country/TerritoryIsrael
CityHaifa
Period27/06/1029/06/10

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