Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptation to the Range in $K$-Armed Bandits   We consider stochastic bandit problems with $K$ arms, each associated with a
bounded distribution supported on the range $[m,M]$. We do not assume that the
range $[m,M]$ is known and show that there is a cost for learning this range.
Indeed, a new trade-off between distribution-dependent and distribution-free
regret bounds arises, which prevents from simultaneously achieving the typical
$\ln T$ and \smash{$\sqrt{T}$} bounds. For instance, a \smash{$\sqrt{T}$}
distribution-free regret bound may only be achieved if the
distribution-dependent regret bounds are at least of order \smash{$\sqrt{T}$}.
We exhibit a strategy achieving the rates for regret indicated by the new
trade-off.

19
The categories of this paper are: eess
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an