Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exp-Concavity of Proper Composite Losses   The goal of online prediction with expert advice is to find a decision
strategy which will perform almost as well as the best expert in a given pool
of experts, on any sequence of outcomes. This problem has been widely studied
and $O(\sqrt{T})$ and $O(\log{T})$ regret bounds can be achieved for convex
losses (\cite{zinkevich2003online}) and strictly convex losses with bounded
first and second derivatives (\cite{hazan2007logarithmic}) respectively. In
special cases like the Aggregating Algorithm (\cite{vovk1995game}) with mixable
losses and the Weighted Average Algorithm (\cite{kivinen1999averaging}) with
exp-concave losses, it is possible to achieve $O(1)$ regret bounds.
\cite{van2012exp} has argued that mixability and exp-concavity are roughly
equivalent under certain conditions. Thus by understanding the underlying
relationship between these two notions we can gain the best of both algorithms
(strong theoretical performance guarantees of the Aggregating Algorithm and the
computational efficiency of the Weighted Average Algorithm). In this paper we
provide a complete characterization of the exp-concavity of any proper
composite loss. Using this characterization and the mixability condition of
proper losses (\cite{van2012mixability}), we show that it is possible to
transform (re-parameterize) any $\beta$-mixable binary proper loss into a
$\beta$-exp-concave composite loss with the same $\beta$. In the multi-class
case, we propose an approximation approach for this transformation.

26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th