Summary of Low-rank Bandits Via Tight Two-to-infinity Singular Subspace Recovery, by Yassir Jedra et al.
Low-Rank Bandits via Tight Two-to-Infinity Singular Subspace Recovery
by Yassir Jedra, William Réveillard, Stefan Stojanovic, Alexandre Proutiere
First submitted to arxiv on: 24 Feb 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 presents efficient algorithms for contextual bandits with low-rank structure. In this setting, a learner observes noisy samples of an unknown reward matrix and must make decisions based on the current context. The proposed algorithms are nearly minimax optimal for policy evaluation, best policy identification, and regret minimization. For instance, the number of samples required to return an ε-optimal policy with probability at least 1-δ typically scales as r(m+n)/ε^2log(1/δ). The regret minimization algorithm enjoys minimax guarantees typically scaling as r(7/4)(m+n)(3/4)√T, which improves over existing algorithms. All the proposed algorithms consist of two phases: first estimating the left and right singular subspaces of the low-rank reward matrix using spectral methods, then reformulating the problems as misspecified linear bandit problems with dimension roughly r(m+n) and misspecification controlled by the subspace recovery error. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how machines can make good decisions when they don’t know everything. It’s like trying to find the best recipe for a cake, but you only get to taste a little bit of each ingredient. The researchers created special algorithms that work really well in this situation. They tested these algorithms and found out that they are very good at making decisions quickly and accurately. This is important because it can help us make better decisions when we don’t have all the information. |
Keywords
* Artificial intelligence * Probability
