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Despite the recent success of representation learning in sequential decisionmaking, the study of the pure exploration scenario (i.e., identify the bestoption and minimize the sample complexity) is still limited. In this paper, westudy multi-task representation learning for best arm identification in linearbandits (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, alltasks share a common low-dimensional linear representation, and our goal is toleverage this feature to accelerate the best arm (policy) identificationprocess for all tasks. For these problems, we design computationally and sampleefficient algorithms DouExpDes and C-DouExpDes, which perform doubleexperimental designs to plan optimal sample allocations for learning the globalrepresentation. We show that by learning the common representation among tasks,our sample complexity is significantly better than that of the native approachwhich solves tasks independently. To the best of our knowledge, this is thefirst work to demonstrate the benefits of representation learning formulti-task pure exploration.

Multi-task Representation Learning for Pure Exploration in Linear Bandits