High-Dimensional Sparse Linear Bandits

Botao Hao; Tor Lattimore; Mengdi Wang

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arXiv · 2011.04020

High-Dimensional Sparse Linear Bandits

Botao Hao·Tor Lattimore·Mengdi Wang

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Abstract

Stochastic linear bandits with high-dimensional sparse features are a practical model for a variety of domains, including personalized medicine and online advertising. We derive a novel $\Omega(n^{2/3})$ dimension-free minimax regret lower bound for sparse linear bandits in the data-poor regime where the horizon is smaller than the ambient dimension and where the feature vectors admit a well-conditioned exploration distribution. This is complemented by a nearly matching upper bound for an explore-then-commit algorithm showing that that $\Theta(n^{2/3})$ is the optimal rate in the data-poor regime. The results complement existing bounds for the data-rich regime and provide another example where carefully balancing the trade-off between information and regret is necessary. Finally, we prove a dimension-free $O(\sqrt{n})$ regret upper bound under an additional assumption on the magnitude of the signal for relevant features.

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stat.ML cs.LG math.ST stat.TH

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BibTeX RIS

Botao Hao, Tor Lattimore, Mengdi Wang. 2020-11-08. High-Dimensional Sparse Linear Bandits. https://arxiv.org/abs/2011.04020

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