Bandit PCA with Minimax Optimal Regret
We study the bandit-feedback version of online principal component analysis (Bandit PCA): in each round $t = 1,\dots,T$, the adversary selects a $d \times d$ symmetric gain matrix $G_t$ with spectrum in $[0,1]$ and rank at most $r$; the learner simultaneously selects a unit vector $w_t \in S^{d-1}$ and receives the reward $w_t^\top G_t w_t$. The learner receives no other feedback, and aims to minimize the regret against the best unit vector in hindsight. This problem was introduced by Kotlowski and Neu (2019), who gave an algorithm with regret $O(d\sqrt{rT \log T})$ and showed the lower bound of $Ω(r\sqrt{T/\log T})$. We improve upon both of these bounds and essentially bridge the gap bet...
| Authors | Moïse Blanchard, Dmitrii Ostrovskii, Aadirupa Saha |
|---|---|
| Primary category | cs.LG |
| Published | 12 July 2026 |
| Last updated at source | 15 July 2026 |
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