Efficient runtime task scheduling on complex memory hierarchy becomes increasingly important as modern and future High-Performance Computing (HPC) systems are progressively composed of multisocket and multi-chiplet nodes with nonuniform memory access latencies. Existing locality-aware scheduling schemes either require control of the data placement policy for memory-bound tasks or maximize locality for all classes of computations, resulting in a loss of potential performance. While such approaches are viable, an adaptive scheduling strategy is preferred to enhance locality and resource sharing efficiency using a portable programming scheme. In this paper, we propose the Adaptive Resource-Moldable Scheduler (ARMS) that dynamically maps a task at runtime to a partition spanning one or more threads, based on the task and DAG requirements. The scheduler builds an online platform-independent model for the local and non-local scheduling costs for each tuple consisting of task type (function) and task topology (task location within DAG). We evaluate ARMS using task-parallel versions of SparseLU, 2D Stencil, FMM, and MatMul as examples. Compared to previous approaches, ARMS achieves up to 3.5x performance gain over state-of-the-art locality-aware scheduling schemes.