  Supervised learning requires the specification of a loss function to
minimise. While the theory of admissible losses from both a computational and
statistical perspective is well-developed, these offer a panoply of different
choices. In practice, this choice is typically made in an \emph{ad hoc} manner.
In hopes of making this procedure more principled, the problem of
\emph{learning the loss function} for a downstream task (e.g., classification)
has garnered recent interest. However, works in this area have been generally
empirical in nature.
  In this paper, we revisit the {\sc SLIsotron} algorithm of Kakade et al.
(2011) through a novel lens, derive a generalisation based on Bregman
divergences, and show how it provides a principled procedure for learning the
loss. In detail, we cast {\sc SLIsotron} as learning a loss from a family of
composite square losses. By interpreting this through the lens of \emph{proper
losses}, we derive a generalisation of {\sc SLIsotron} based on Bregman
divergences. The resulting {\sc BregmanTron} algorithm jointly learns the loss
along with the classifier. It comes equipped with a simple guarantee of
convergence for the loss it learns, and its set of possible outputs comes with
a guarantee of agnostic approximability of Bayes rule. Experiments indicate
that the {\sc BregmanTron} substantially outperforms the {\sc SLIsotron}, and
that the loss it learns can be minimized by other algorithms for different
tasks, thereby opening the interesting problem of \textit{loss transfer}
between domains.
