革新知能統合研究センター

Title: Meta-Learning Representations with Contextual Linear Bandits

Abstract:
Abstract: Meta-learning seeks to build algorithms that rapidly learn how to solve new learning problems based on previous experience. In this paper we investigate meta-learning in the setting of stochastic linear bandit tasks. We assume that the tasks share a low dimensional representation, which has been partially acquired from previous learning tasks. We aim to leverage this information in order to learn a new downstream bandit task, which shares the same representation. Our principal contribution is to show that if the learned representation estimates well the unknown one, then the downstream task can be efficiently learned by a greedy policy that we propose in this work. We derive an upper bound on the regret of this policy, which is, up to logarithmic factors, of order $sqrt{rN}(1vee sqrt{d/T})$, where $N$ is the horizon of the downstream task, $T$ is the number of training tasks, $d$ the ambient dimension and $r ll d$ the dimension of the representation. We highlight that our strategy does not need to know $r$. We note that if $T> d$ our bound achieves the same rate of optimal minimax bandit algorithms using the true underlying representation (up to a logarithmic term).
This is a joint work with Leonardo Cella and Massimiliano Pontil.

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