UniRank: Unimodal Bandit Algorithm for Online Ranking
This work addresses an incremental improvement in online ranking algorithms for applications like recommendation systems, focusing on more efficient user comparisons.
The paper tackles the problem of finding an optimal monopartite matching in a weighted graph using a semi-bandit approach, reducing the expected regret bound from O(L log(L)/Δ log(T)) to O(L Δ/Δ̃² log(T)) with theoretical and experimental validation.
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 $O(\frac{L\log(L)}Δ\log(T))$ 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 $O(L\frac{1}Δ\log(T))$. Secondly, we show that by moving the focus towards the main question `\emph{Is user $i$ better than user $j$?}' this regret becomes $O(L\fracΔ{\tildeΔ^2}\log(T))$, where $\TildeΔ > Δ$ derives from a better way of comparing users. Some experimental results finally show these theoretical results are corroborated in practice.