We study the problem of assigning operations in a dataflow graph to devices to minimize execution time in a work-conserving system, with emphasis on complex machine learning workloads. Prior learning-based methods often struggle due to three key limitations: (1) reliance on bulk-synchronous systems like TensorFlow, which under-utilize devices due to barrier synchronization; (2) lack of awareness of the scheduling mechanism of underlying systems when designing learning-based methods; and (3) exclusive dependence on reinforcement learning, ignoring the structure of effective heuristics designed by experts. In this paper, we propose \textsc{Doppler}, a three-stage framework for training dual-policy networks consisting of 1) a $\mathsf{SEL}$ policy for selecting operations and 2) a $\mathsf{PLC}$ policy for placing chosen operations on devices. Our experiments show that \textsc{Doppler} outperforms all baseline methods across tasks by reducing system execution time and additionally demonstrates sampling efficiency by reducing per-episode training time.