TY - JOUR A1 - Kerdreux, Thomas A1 - Roux, Christophe A1 - d'Aspremont, Alexandre A1 - Pokutta, Sebastian T1 - Linear Bandits on Uniformly Convex Sets T2 - Journal of Machine Learning Research N2 - Linear bandit algorithms yield O~(n√T) pseudo-regret bounds on compact convex action sets K⊂Rn and two types of structural assumptions lead to better pseudo-regret bounds. When K is the simplex or an ℓp ball with p∈]1,2], there exist bandits algorithms with O~(√n√T) pseudo-regret bounds. Here, we derive bandit algorithms for some strongly convex sets beyond ℓp balls that enjoy pseudo-regret bounds of O~(√n√T), which answers an open question from [BCB12, §5.5.]. Interestingly, when the action set is uniformly convex but not necessarily strongly convex, we obtain pseudo-regret bounds with a dimension dependency smaller than O(√n). However, this comes at the expense of asymptotic rates in T varying between O(√T) and O(T). Y1 - 2021 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8398 UR - https://www.jmlr.org/papers/v22/21-0277.html VL - 22 IS - 284 SP - 1 EP - 23 ER -