  Despite the recent success of representation learning in sequential decision
making, the study of the pure exploration scenario (i.e., identify the best
option and minimize the sample complexity) is still limited. In this paper, we
study multi-task representation learning for best arm identification in linear
bandits (RepBAI-LB) and best policy identification in contextual linear bandits
(RepBPI-CLB), two popular pure exploration settings with wide applications,
e.g., clinical trials and web content optimization. In these two problems, all
tasks share a common low-dimensional linear representation, and our goal is to
leverage this feature to accelerate the best arm (policy) identification
process for all tasks. For these problems, we design computationally and sample
efficient algorithms DouExpDes and C-DouExpDes, which perform double
experimental designs to plan optimal sample allocations for learning the global
representation. We show that by learning the common representation among tasks,
our sample complexity is significantly better than that of the native approach
which solves tasks independently. To the best of our knowledge, this is the
first work to demonstrate the benefits of representation learning for
multi-task pure exploration.
