Mobile edge computing facilitates users to offload computation tasks to edge servers for meeting their stringent delay requirements. Previous works mainly explore task offloading when system-side information is given (e.g., server processing speed, cellular data rate), or centralized offloading under system uncertainty. But both generally fall short to handle task placement involving many coexisting users in a dynamic and uncertain environment. In this paper, we develop a multi-user offloading framework considering unknown yet stochastic system-side information to enable a decentralized user-initiated service placement. Specifically, we formulate the dynamic task placement as an online multi-user multi-armed bandit process, and propose a decentralized epoch based offloading (DEBO) to optimize user rewards which are subjected under network delay. We show that DEBO can deduce the optimal user-server assignment, thereby achieving a close-to-optimal service performance and tight O(log T) offloading regret. Moreover, we generalize DEBO to various common scenarios such as unknown reward gap, dynamic entering or leaving of clients, and fair reward distribution, while further exploring when users' offloaded tasks require heterogeneous computing resources. Particularly, we accomplish a sub-linear regret for each of these instances. Real measurements based evaluations corroborate the superiority of our offloading schemes over state-of-the-art approaches in optimizing delay-sensitive rewards.