Follow the leader if you can, hedge if you must
de Rooij, Steven, van Erven, Tim, Grünwald, Peter D., & Koolen, Wouter M. (2014) Follow the leader if you can, hedge if you must. Journal of Machine Learning Research, 15, pp. 1281-1316.
Follow-the-Leader (FTL) is an intuitive sequential prediction strategy that guarantees constant regret in the stochastic setting, but has poor performance for worst-case data. Other hedging strategies have better worst-case guarantees but may perform much worse than FTL if the data are not maximally adversarial. We introduce the FlipFlop algorithm, which is the first method that provably combines the best of both worlds. As a stepping stone for our analysis, we develop AdaHedge, which is a new way of dynamically tuning the learning rate in Hedge without using the doubling trick. AdaHedge refines a method by Cesa-Bianchi, Mansour, and Stoltz (2007), yielding improved worst-case guarantees. By interleaving AdaHedge and FTL, FlipFlop achieves regret within a constant factor of the FTL regret, without sacrificing AdaHedge’s worst-case guarantees. AdaHedge and FlipFlop do not need to know the range of the losses in advance; moreover, unlike earlier methods, both have the intuitive property that the issued weights are invariant under rescaling and translation of the losses. The losses are also allowed to be negative, in which case they may be interpreted as gains.
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|Item Type:||Journal Article|
|Keywords:||Hedge, learning rate, mixability, online learning, prediction with expert advice|
|Divisions:||Current > QUT Faculties and Divisions > Science & Engineering Faculty
Past > Schools > Mathematical Sciences
|Copyright Owner:||Copyright 2014 Steven de Rooij, Tim van Erven, Peter D. Grünwald and Wouter M. Koolen|
|Deposited On:||30 Jun 2014 22:53|
|Last Modified:||26 May 2015 22:05|
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