Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Converse Result on Convergence Time for Opportunistic Wireless
  Scheduling   This paper proves an impossibility result for stochastic network utility
maximization for multi-user wireless systems, including multiple access and
broadcast systems. Every time slot an access point observes the current channel
states for each user and opportunistically selects a vector of transmission
rates. Channel state vectors are assumed to be independent and identically
distributed with an unknown probability distribution. The goal is to learn to
make decisions over time that maximize a concave utility function of the
running time average transmission rate of each user. Recently it was shown that
a stochastic Frank-Wolfe algorithm converges to utility-optimality with an
error of $O(\log(T)/T)$, where $T$ is the time the algorithm has been running.
An existing $\Omega(1/T)$ converse is known. The current paper improves the
converse to $\Omega(\log(T)/T)$, which matches the known achievability result.
It does this by constructing a particular (simple) system for which no
algorithm can achieve a better performance. The proof uses a novel reduction of
the opportunistic scheduling problem to a problem of estimating a Bernoulli
probability $p$ from independent and identically distributed samples. Along the
way we refine a regret bound for Bernoulli estimation to show that, for any
sequence of estimators, the set of values $p \in [0,1]$ under which the
estimators perform poorly has measure at least $1/8$.

26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ