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Mirror Descent Meets Fixed Share (and feels no regret)

Abstract : Mirror descent with an entropic regularizer is known to achieve shifting regret bounds that are logarithmic in the dimension. This is done using either a carefully designed projection or by a weight sharing technique. Via a novel unified analysis, we show that these two approaches deliver essentially equivalent bounds on a notion of regret generalizing shifting, adaptive, discounted, and other related regrets. Our analysis also captures and extends the generalized weight sharing technique of Bousquet and Warmuth, and can be refined in several ways, including improvements for small losses and adaptive tuning of parameters.
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Contributor : Gilles Stoltz <>
Submitted on : Thursday, September 27, 2012 - 2:51:59 PM
Last modification on : Tuesday, September 22, 2020 - 3:49:34 AM
Long-term archiving on: : Friday, December 28, 2012 - 6:20:08 AM


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  • HAL Id : hal-00670514, version 2
  • ARXIV : 1202.3323



Nicolò Cesa-Bianchi, Pierre Gaillard, Gabor Lugosi, Gilles Stoltz. Mirror Descent Meets Fixed Share (and feels no regret). NIPS 2012, Dec 2012, Lake Tahoe, United States. Paper 471. ⟨hal-00670514v2⟩



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