Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints

Yuantong Li, Guang Cheng, Xiaowu Dai
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:27589-27614, 2024.

Abstract

In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided online matching markets with complementary preferences and quota constraints, where agents’ preferences are unknown a priori and must be learned from data. The presence of mixed quota and complementary preferences constraints can lead to instability in the matching process, making this problem challenging to solve. To overcome this challenge, we formulate the problem as a bandit learning framework and propose the Multi-agent Multi-type Thompson Sampling (MMTS) algorithm. The algorithm combines the strengths of Thompson Sampling for exploration with a new double matching technique to provide a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability and has a total $\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret with high probability, which exhibits linearity with respect to the total firm’s quota $Q$, the square root of the maximum size of available type workers $\sqrt{K_{\max}}$ and time horizon $T$. In addition, simulation studies also demonstrate MMTS’ effectiveness in various settings. We provide code used in our experiments https://github.com/Likelyt/Double-Matching.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-li24n, title = {Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints}, author = {Li, Yuantong and Cheng, Guang and Dai, Xiaowu}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {27589--27614}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/li24n/li24n.pdf}, url = {https://proceedings.mlr.press/v235/li24n.html}, abstract = {In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided online matching markets with complementary preferences and quota constraints, where agents’ preferences are unknown a priori and must be learned from data. The presence of mixed quota and complementary preferences constraints can lead to instability in the matching process, making this problem challenging to solve. To overcome this challenge, we formulate the problem as a bandit learning framework and propose the Multi-agent Multi-type Thompson Sampling (MMTS) algorithm. The algorithm combines the strengths of Thompson Sampling for exploration with a new double matching technique to provide a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability and has a total $\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret with high probability, which exhibits linearity with respect to the total firm’s quota $Q$, the square root of the maximum size of available type workers $\sqrt{K_{\max}}$ and time horizon $T$. In addition, simulation studies also demonstrate MMTS’ effectiveness in various settings. We provide code used in our experiments https://github.com/Likelyt/Double-Matching.} }
Endnote
%0 Conference Paper %T Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints %A Yuantong Li %A Guang Cheng %A Xiaowu Dai %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-li24n %I PMLR %P 27589--27614 %U https://proceedings.mlr.press/v235/li24n.html %V 235 %X In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided online matching markets with complementary preferences and quota constraints, where agents’ preferences are unknown a priori and must be learned from data. The presence of mixed quota and complementary preferences constraints can lead to instability in the matching process, making this problem challenging to solve. To overcome this challenge, we formulate the problem as a bandit learning framework and propose the Multi-agent Multi-type Thompson Sampling (MMTS) algorithm. The algorithm combines the strengths of Thompson Sampling for exploration with a new double matching technique to provide a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability and has a total $\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret with high probability, which exhibits linearity with respect to the total firm’s quota $Q$, the square root of the maximum size of available type workers $\sqrt{K_{\max}}$ and time horizon $T$. In addition, simulation studies also demonstrate MMTS’ effectiveness in various settings. We provide code used in our experiments https://github.com/Likelyt/Double-Matching.
APA
Li, Y., Cheng, G. & Dai, X.. (2024). Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:27589-27614 Available from https://proceedings.mlr.press/v235/li24n.html.

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