The problem of coordinated data collection is studied for a mobile crowdsensing (MCS) system. A mobile crowdsensing platform (MCSP) sequentially publishes sensing tasks to the available mobile units (MUs) that signal their willingness to participate in a task by sending sensing offers back to the MCSP. From the received offers, the MCSP decides the task assignment. A stable task assignment must address two challenges: the MCSP's and MUs' conflicting goals, and the uncertainty about the MUs' required efforts and preferences. To overcome these challenges a novel decentralized approach combining matching theory and online learning, called collision-avoidance multi-armed bandit with strategic free sensing (CA-MAB-SFS), is proposed. The task assignment problem is modeled as a matching game considering the MCSP's and MUs' individual goals while the MUs learn their efforts online. Our innovative "free-sensing" mechanism significantly improves the MU's learning process while reducing collisions during task allocation. The stable regret of CA-MAB-SFS, i.e., the loss of learning, is analytically shown to be bounded by a sublinear function, ensuring the convergence to a stable optimal solution. Simulation results show that CA-MAB-SFS increases the MUs' and the MCSP's satisfaction compared to state-of-the-art methods while reducing the average task completion time by at least 16%.

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