We tackle a new emerging problem, which is finding an optimal monopartite
matching in a weighted graph. The semi-bandit version, where a full matching is
sampled at each iteration, has been addressed by \cite{ADMA}, creating an
algorithm with an expected regret matching O(ΔLlog(L)log(T))
with 2L players, T iterations and a minimum reward gap Δ. We reduce
this bound in two steps. First, as in \cite{GRAB} and \cite{UniRank} we use the
unimodality property of the expected reward on the appropriate graph to design
an algorithm with a regret in O(LΔ1log(T)). Secondly, we show
that by moving the focus towards the main question `\emph{Is user i better
than user j?}' this regret becomes
O(LΔ~2Δlog(T)), where \Tilde{\Delta} > \Delta
derives from a better way of comparing users. Some experimental results finally
show these theoretical results are corroborated in practice