Generalised Mixability, Constant Regret, and Bayesian Updating

Reid, Mark D., Frongillo, Rafael M., Williamson, Robert C.

arXiv.org Machine Learning 

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 $\Phi$-mixability where the Bregman divergence $D_\Phi$ replaces the KL divergence. We prove that losses that are $\Phi$-mixable also enjoy constant regret bounds via a generalised aggregating algorithm that is similar to mirror descent.

Duplicate Docs Excel Report

Title
None found

Similar Docs  Excel Report  more

TitleSimilaritySource
None found