Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Competitive on-line learning with a convex loss function   We consider the problem of sequential decision making under uncertainty in
which the loss caused by a decision depends on the following binary
observation. In competitive on-line learning, the goal is to design decision
algorithms that are almost as good as the best decision rules in a wide
benchmark class, without making any assumptions about the way the observations
are generated. However, standard algorithms in this area can only deal with
finite-dimensional (often countable) benchmark classes. In this paper we give
similar results for decision rules ranging over an arbitrary reproducing kernel
Hilbert space. For example, it is shown that for a wide class of loss functions
(including the standard square, absolute, and log loss functions) the average
loss of the master algorithm, over the first $N$ observations, does not exceed
the average loss of the best decision rule with a bounded norm plus
$O(N^{-1/2})$. Our proof technique is very different from the standard ones and
is based on recent results about defensive forecasting. Given the probabilities
produced by a defensive forecasting algorithm, which are known to be well
calibrated and to have good resolution in the long run, we use the expected
loss minimization principle to find a suitable decision.

32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
19
The categories of this paper are: eess
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg