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arXiv · 1403.2433

Generalised Mixability, Constant Regret, and Bayesian Updating

Mark D. Reid·Rafael M. Frongillo·Robert C. Williamson
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Abstract

Mixability of a loss is known to characterise when constant regret bounds are achievable in games of prediction with expert advice through the use of Vovk's aggregating algorithm. We provide a new interpretation of mixability via convex analysis that highlights the role of the Kullback-Leibler divergence in its definition. This naturally generalises to what we call $Φ$-mixability where the Bregman divergence $D_Φ$ replaces the KL divergence. We prove that losses that are $Φ$-mixable also enjoy constant regret bounds via a generalised aggregating algorithm that is similar to mirror descent.

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Mark D. Reid, Rafael M. Frongillo, Robert C. Williamson. 2014-03-10. Generalised Mixability, Constant Regret, and Bayesian Updating. https://arxiv.org/abs/1403.2433

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