Unimodal Mono-Partite Matching in a Bandit Setting
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.01511
- arXiv:
- arXiv:2208.01511
- Bibcode:
- 2022arXiv220801511G
- Keywords:
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- Computer Science - Machine Learning;
- Computer Science - Data Structures and Algorithms
- E-Print:
- Complex Feedback in Online Learning Workshop at the 39th International Conference on Machine Learning, Jul 2022, Baltimore, United States