Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Rates of Convergence in Learning of Optimal Temporally Fair
  Schedulers   Multi-user schedulers are designed to achieve optimal average system utility
(e.g. throughput) subject to a set of fairness criteria. In this work,
scheduling under temporal fairness constraints is considered. Prior works have
shown that a class of scheduling strategies called threshold based strategies
(TBSs) achieve optimal system utility under temporal fairness constraints. The
optimal TBS thresholds are determined as a function of the channel statistics.
In order to provide performance guarantees for TBSs in practical scenarios ---
where the scheduler learns the optimal thresholds based on the empirical
observations of the channel realizations --- it is necessary to evaluate the
rates of convergence of TBS thresholds to the optimal value. In this work,
these rates of convergence and the effect on the resulting system utility are
investigated. It is shown that the best estimate of the threshold vector is at
least $\omega(\frac{1}{\sqrt{t}})$ away from the optimal value, where $t$ is
the number of observations of the independent and identically distributed
channel realizations. Furthermore, it is shown that under long-term fairness
constraints, the scheduler may achieve an average utility that is higher than
the optimal long-term utility by violating the fairness criteria for a long
initial period. Consequently, the resulting system utility may converge to its
optimal long-term value from above. The results are verified by providing
simulations of practical scheduling scenarios.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph