Summary of Matrix Sketching in Bandits: Current Pitfalls and New Framework, by Dongxie Wen et al.
Matrix Sketching in Bandits: Current Pitfalls and New Framework
by Dongxie Wen, Hanyan Yin, Xiao Zhang, Zhewei Wei
First submitted to arxiv on: 14 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper revisits the application of sketching techniques in linear bandits, focusing on improving efficiency while addressing critical pitfalls. Current approaches leverage matrix sketching to reduce time complexity from O(d^2) to O(d), but may encounter linear regret if the spectral tail of the covariance matrix does not decrease rapidly. The authors propose Dyadic Block Sketching, an innovative streaming matrix sketching approach that adaptively manages sketch size to constrain global spectral loss, ensuring efficiency and tracking the best rank-k approximation online. This method achieves sublinear regret without prior knowledge of the covariance matrix, even under the worst-case scenario. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how to make online learning more efficient using a technique called sketching. Right now, most approaches use something called matrix sketching to make things faster, but they can get stuck if the data doesn’t decrease quickly enough. The authors come up with a new way to do this called Dyadic Block Sketching that adjusts itself to keep things under control and makes sure it’s finding the best solution possible. This helps it learn more quickly and accurately without needing to know too much about the data beforehand. |
Keywords
» Artificial intelligence » Online learning » Tracking
