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Adaptive Hedge
Tim van Erven · Peter Grünwald · Wouter M Koolen · Steven D Rooij

Tue Dec 13 08:45 AM -- 02:59 PM (PST) @ None #None

Most methods for decision-theoretic online learning are based on the Hedge algorithm, which takes a parameter called the learning rate. In most previous analyses the learning rate was carefully tuned to obtain optimal worst-case performance, leading to suboptimal performance on easy instances, for example when there exists an action that is significantly better than all others. We propose a new way of setting the learning rate, which adapts to the difficulty of the learning problem: in the worst case our procedure still guarantees optimal performance, but on easy instances it achieves much smaller regret. In particular, our adaptive method achieves constant regret in a probabilistic setting, when there exists an action that on average obtains strictly smaller loss than all other actions. We also provide a simulation study comparing our approach to existing methods.

Author Information

Tim van Erven (Leiden University)
Peter Grünwald (CWI and Leiden University)
Wouter M Koolen (Centrum Wiskunde & Informatica)
Steven D Rooij (CWI)

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