As representation learning becomes a powerful technique to reduce sample complexity in reinforcement learning (RL) in practice, theoretical understanding of its advantage is still limited. In this paper, we theoretically characterize the benefit of representation learning under the low-rank Markov decision process (MDP) model. We first study multitask low-rank RL (as upstream training), where all tasks share a common representation, and propose a new multitask reward-free algorithm called REFUEL. REFUEL learns both the transition kernel and the near-optimal policy for each task, and outputs a well-learned representation for downstream tasks. Our result demonstrates that multitask representation learning is provably more sample-efficient than learning each task individually, as long as the total number of tasks is above a certain threshold. We then study the downstream RL in both online and offline settings, where the agent is assigned with a new task sharing the same representation as the upstream tasks. For both online and offline settings, we develop a sample-efficient algorithm, and show that it finds a near-optimal policy with the suboptimality gap bounded by the sum of the estimation error of the learned representation in upstream and a vanishing term as the number of downstream samples becomes large. Our downstream results of online and offline RL further capture the benefit of employing the learned representation from upstream as opposed to learning the representation of the low-rank model directly. To the best of our knowledge, this is the first theoretical study that characterizes the benefit of representation learning in exploration-based reward-free multitask RL for both upstream and downstream tasks.

本文首次从理论上研究了使用多任务表示学习来提高勘探性无奖励多任务强化学习中多个任务的样本效率，并证明了它比单独学习每个任务更加样本高效。此外，我们还研究了下游强化学习，并表明与直接学习低秩模型有所不同的是，从上游学习的表示更有利于下游强化学习。

多任务表示学习在强化学习中的证明收益