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In sparse linear bandits, a learning agent sequentially selects an action andreceive reward feedback, and the reward function depends linearly on a fewcoordinates of the covariates of the actions. This has applications in manyreal-world sequential decision making problems. In this paper, we propose asimple and computationally efficient sparse linear estimation method calledPopArt that enjoys a tighter $\ell_1$ recovery guarantee compared to Lasso(Tibshirani, 1996) in many problems. Our bound naturally motivates anexperimental design criterion that is convex and thus computationally efficientto solve. Based on our novel estimator and design criterion, we derive sparselinear bandit algorithms that enjoy improved regret upper bounds upon the stateof the art (Hao et al., 2020), especially w.r.t. the geometry of the givenaction set. Finally, we prove a matching lower bound for sparse linear banditsin the data-poor regime, which closes the gap between upper and lower bounds inprior work.

PopArt: Efficient Sparse Regression and Experimental Design for Optimal Sparse Linear Bandits