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Stationary low-rank bandits exploit rank but break under subspace change; non-stationary linear bandits adapt to drift but pay ambient rate $\\widetilde{O}(d\\sqrt{T})$. We study piecewise-stationary low-rank linear contextual bandits with scalar feedback: $\\theta_t = B_k^\\star w_t$ with rank-$r$ factor $B_k^\\star\\in\\mathbb{R}^{d\\times r}$ constant within each of $K$ unknown segments and able to shift at boundaries. Our results are tight along three axes. (i) Identification boundary. With single-play scalar rewards, the moving subspace is recoverable through quadratic functionals of rewards iff three probe-side conditions hold: known noise variance, bounded state-noise coupling, and full-dimensional probe support. Each is necessary in the","title":"Catching a Moving Subspace: Low-Rank Bandits Beyond Stationarity","url":"https://arxiv.org/abs/2605.20269","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.20269v1 Announce Type: cross \nAbstract: Many bandit deployments (recommendation, clinical dosing, ad targeting) share two facts prior work handles only in isolation: rewards live on a low-dimensional latent subspace, and that subspace drifts. Stationary low-rank bandits exploit rank but break under subspace change; non-stationary linear bandits adapt to drift but pay ambient rate $\\widetilde{O}(d\\sqrt{T})$. We study piecewise-stationary low-rank linear contextual bandits with scalar feedback: $\\theta_t = B_k^\\star w_t$ with rank-$r$ factor $B_k^\\star\\in\\mathbb{R}^{d\\times r}$ constant within each of $K$ unknown segments and able to shift at boundaries. Our results are tight along three axes. (i) Identification boundary. With single-play scalar rewards, the moving subspace is recoverable through quadratic functionals of rewards iff three probe-side conditions hold: known noise variance, bounded state-noise coupling, and full-dimensional probe support. 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