Stochastic Matching Bandits with Rare Optimization Updates
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912858772602880 |
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| author | Kim, Jung-hun Oh, Min-hwan |
| author_facet | Kim, Jung-hun Oh, Min-hwan |
| contents | We introduce a bandit framework for stochastic matching under the multinomial logit (MNL) choice model. In our setting, $N$ agents on one side are assigned to $K$ arms on the other side, where each arm stochastically selects an agent from its assigned pool according to unknown preferences and yields a corresponding reward over a horizon $T$. The objective is to minimize regret by maximizing the cumulative revenue from successful matches. A naive approach requires solving an NP-hard combinatorial optimization problem at every round, resulting in a prohibitive computational cost. To address this challenge, we propose batched algorithms that strategically limit the number of times matching assignments are updated to $Θ(\log\log T)$ over the entire horizon. By invoking expensive combinatorial optimization only on a vanishing fraction of rounds, our algorithms substantially reduce overall computational overhead while still achieving a regret bound of $\widetilde{\mathcal{O}}(\sqrt{T})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Matching Bandits with Rare Optimization Updates Kim, Jung-hun Oh, Min-hwan Machine Learning We introduce a bandit framework for stochastic matching under the multinomial logit (MNL) choice model. In our setting, $N$ agents on one side are assigned to $K$ arms on the other side, where each arm stochastically selects an agent from its assigned pool according to unknown preferences and yields a corresponding reward over a horizon $T$. The objective is to minimize regret by maximizing the cumulative revenue from successful matches. A naive approach requires solving an NP-hard combinatorial optimization problem at every round, resulting in a prohibitive computational cost. To address this challenge, we propose batched algorithms that strategically limit the number of times matching assignments are updated to $Θ(\log\log T)$ over the entire horizon. By invoking expensive combinatorial optimization only on a vanishing fraction of rounds, our algorithms substantially reduce overall computational overhead while still achieving a regret bound of $\widetilde{\mathcal{O}}(\sqrt{T})$. |
| title | Stochastic Matching Bandits with Rare Optimization Updates |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.04194 |