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Nowadays, the Hierarchical Storage System (HSS) is considered as an ideal model to meet the cost-performance demand. The data migration between storing tiers of HSS is the way to achieve the cost-performance goal. The bandwidth control is to limit the maximum amount of data migration. Most of previous research about HSS focus on studying the data migration policy instead of bandwidth control. However, the recent research about cache and networking optimization suggest that the bandwidth control has significant impact on the system performance. Few previous work achieves a satisfactory bandwidth control in HSS since it is hard to control bandwidth for so many data migration tasks simultaneously. In this paper, we first give a stochastic programming model to formalize the bandwidth control problem in HSS. Then we propose a learning-aided bandwidth control policy for HSS, named \Pascal{}, which learns to control the bandwidth of different data migration task in an cooperative way. We implement \Pascal{} on a commercial HSS and compare it with three strong baselines over a group of workloads. Our evaluation on the physical system shows that \Pascal{} can effectively decrease 1.95X the tail latency and greatly improve throughput stability (2X \(\downarrow\) throughput jitter), and meanwhile keep the throughput at a relatively high level.