Contents of Appendix A Extended Literature Review 14 B Time Uniform Lasso Analysis 15 C Results on Exploration 18 C.1 ALE

Table 2 compares recent work on sparse linear bandits based on a number of important factors. Some of the mentioned bounds depend on problem-dependent parameters (e.g. Carpentier and Munos [ 2012 ] assume that the action set is a Euclidean ball, and that the noise is directly added to the parameter vector, i.e. In this setting, Carpentier and Munos [ 2012 ] present a O ( d p n) regret bound. Li et al. [ 2022 ] require a stronger condition This is generally not true, but may hold with high probability.