  In this work we investigate meta-learning (or learning-to-learn) approaches
in multi-task linear stochastic bandit problems that can originate from
multiple environments. Inspired by the work of [1] on meta-learning in a
sequence of linear bandit problems whose parameters are sampled from a single
distribution (i.e., a single environment), here we consider the feasibility of
meta-learning when task parameters are drawn from a mixture distribution
instead. For this problem, we propose a regularized version of the OFUL
algorithm that, when trained on tasks with labeled environments, achieves low
regret on a new task without requiring knowledge of the environment from which
the new task originates. Specifically, our regret bound for the new algorithm
captures the effect of environment misclassification and highlights the
benefits over learning each task separately or meta-learning without
recognition of the distinct mixture components.
