  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.
