A Second-order Bound with Excess Losses

Pierre Gaillard 1, 2 Gilles Stoltz 1 Tim van Erven 3, 4
3 SELECT - Model selection in statistical learning
Inria Saclay - Ile de France, LMO - Laboratoire de Mathématiques d'Orsay, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : We study online aggregation of the predictions of experts, and first show new second-order regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorithm) with multiple learning rates. These bounds are in terms of excess losses, the differences between the instantaneous losses suffered by the algorithm and the ones of a given expert. We then demonstrate the interest of these bounds in the context of experts that report their confidences as a number in the interval [0,1] using a generic reduction to the standard setting. We conclude by two other applications in the standard setting, which improve the known bounds in case of small excess losses and show a bounded regret against i.i.d. sequences of losses.
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Contributor : Gilles Stoltz <>
Submitted on : Saturday, February 8, 2014 - 10:32:27 AM
Last modification on : Wednesday, January 23, 2019 - 2:39:21 PM
Long-term archiving on : Thursday, May 8, 2014 - 11:50:10 PM


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  • HAL Id : hal-00943665, version 1
  • ARXIV : 1402.2044



Pierre Gaillard, Gilles Stoltz, Tim van Erven. A Second-order Bound with Excess Losses. 2014. ⟨hal-00943665⟩



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