Visual Simultaneous Localization and Mapping (vSLAM) is a prevailing technology for many emerging robotic applications. Achieving real-time SLAM on mobile robotic systems with limited computational resources is challenging because the complexity of SLAM algorithms increases over time. This restriction can be lifted by offloading computations to edge servers, forming the emerging paradigm of edge-assisted SLAM. Nevertheless, the exogenous and stochastic input processes affect the dynamics of the edge-assisted SLAM system. Moreover, the requirements of clients on SLAM metrics change over time, exerting implicit and time-varying effects on the system. In this paper, we aim to push the limit beyond existing edge-assist SLAM by proposing a new architecture that can handle the input-driven processes and also satisfy clients' implicit and time-varying requirements. The key innovations of our work involve a regional feature prediction method for importance-aware local data processing, a configuration adaptation policy that integrates data compression/decompression and task offloading, and an input-dependent learning framework for task scheduling with constraint satisfaction. Extensive experiments prove that our architecture improves pose estimation accuracy and saves up to 47% of communication costs compared with a popular edge-assisted SLAM system, as well as effectively satisfies the clients' requirements.