Unimodal Mono-Partite Matching in a Bandit Setting - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2022

Unimodal Mono-Partite Matching in a Bandit Setting

Résumé

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 $O(\frac{L\log(L)}{\Delta}\log(T))$ with $2L$ players, $T$ iterations and a minimum reward gap $\Delta$. 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 $O(L\frac{1}{\Delta}\log(T))$. Secondly, we show that by moving the focus towards the main question `\emph{Is user $i$ better than user $j$?}' this regret becomes $O(L\frac{\Delta}{\tilde{\Delta}^2}\log(T))$, where $\Tilde{\Delta} > \Delta$ derives from a better way of comparing users. Some experimental results finally show these theoretical results are corroborated in practice.
Fichier principal
Vignette du fichier
main.pdf (356.13 Ko) Télécharger le fichier
main.synctex.gz (157.06 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03740961 , version 1 (02-08-2022)

Identifiants

Citer

Matthieu Rodet, Romaric Gaudel. Unimodal Mono-Partite Matching in a Bandit Setting. Complex Feedback in Online Learning Workshop at the 39th International Conference on Machine Learning, Jul 2022, Baltimore, United States. ⟨hal-03740961⟩
64 Consultations
12 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More