## 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. 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. Such global cost functions include the makespan (the maximum over the alternatives) and the L_{d} norm (over the alternatives). Based on approachability theory, we design an algorithm that guarantees vanishing regret for this setting, where the regret is measured with respect to the best static decision that selects the same distribution over alternatives at every time step. For the special case of makespan cost we devise a simple and efficient algorithm. In contrast, we show that for concave global cost functions, such as L_{d} norms for d < 1, the worst-case average regret does not vanish.

Original language | English |
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State | Published - 2009 |

Event | 22nd Conference on Learning Theory, COLT 2009 - Montreal, QC, Canada Duration: 18 Jun 2009 → 21 Jun 2009 |

### Conference

Conference | 22nd Conference on Learning Theory, COLT 2009 |
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Country/Territory | Canada |

City | Montreal, QC |

Period | 18/06/09 → 21/06/09 |