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About this paper
Zhiyuan Tang, Wanning Chen, Kan Xu
This research provides optimal theoretical guarantees for low-rank matrix completion when observations are dependent due to "matching interference" in two-sided markets, a challenge violating standard matrix completion assumptions. The study extends these insights to online learning, developing algorithms that achieve substantially improved regret bounds for optimal and stable matching problems.
Key insights
- Nuclear norm regularization remains effective and achieves near-optimal Frobenius norm error bounds even with dependent observations from matching interference.
- A specialized double-enhancement procedure is essential for obtaining sharp entry-wise error guarantees for individual reward estimates.
- Leveraging the low-rank structure through matrix completion significantly reduces the dependence on market dimensions and improves regret bounds in online matching problems.
Summary by alphaXiv.
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