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Meta-learning seeks to build algorithms that rapidly learn how to solve newlearning problems based on previous experience. In this paper we investigatemeta-learning in the setting of stochastic linear bandit tasks. We assume thatthe tasks share a low dimensional representation, which has been partiallyacquired from previous learning tasks. We aim to leverage this information inorder to learn a new downstream bandit task, which shares the samerepresentation. Our principal contribution is to show that if the learnedrepresentation estimates well the unknown one, then the downstream task can beefficiently learned by a greedy policy that we propose in this work. We derivean upper bound on the regret of this policy, which is, up to logarithmicfactors, of order $r\sqrt{N}(1\vee \sqrt{d/T})$, where $N$ is the horizon ofthe downstream task, $T$ is the number of training tasks, $d$ the ambientdimension and $r \ll d$ the dimension of the representation. We highlight thatour strategy does not need to know $r$. We note that if $T> d$ our boundachieves the same rate of optimal minimax bandit algorithms using the trueunderlying representation. Our analysis is inspired and builds in part uponprevious work on meta-learning in the i.i.d. full information setting\citep{tripuraneni2021provable,boursier2022trace}. As a separate contributionwe show how to relax certain assumptions in those works, thereby improvingtheir representation learning and risk analysis.

Meta Representation Learning with Contextual Linear Bandits