In this paper, we employ multiple UAVs to accelerate data transmissions from ground users (GUs) to a remote base station (BS) via the UAVs' relay communications. The UAVs' intermittent information exchanges typically result in delays in acquiring the complete system state and hinder their effective collaboration. To maximize the overall throughput, we first propose a delay-tolerant multi-agent deep reinforcement learning (MADRL) algorithm that integrates a delay-penalized reward to encourage information sharing among UAVs, while jointly optimizing the UAVs' trajectory planning, network formation, and transmission control strategies. Additionally, considering information loss due to unreliable channel conditions, we further propose a spatio-temporal attention based prediction approach to recover the lost information and enhance each UAV's awareness of the network state. These two designs are envisioned to enhance the network capacity in UAV-assisted wireless networks with limited communications. The simulation results reveal that our new approach achieves over 50\% reduction in information delay and 75% throughput gain compared to the conventional MADRL. Interestingly, it is shown that improving the UAVs' information sharing will not sacrifice the network capacity. Instead, it significantly improves the learning performance and throughput simultaneously. It is also effective in reducing the need for UAVs' information exchange and thus fostering practical deployment of MADRL in UAV-assisted wireless networks.

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