Modern systems-on-chip (SoCs) use dynamic power management (DPM) techniques to improve energy efficiency. However, existing techniques are unable to efficiently adapt the runtime decisions considering multiple objectives (e.g., energy and real-time requirements) simultaneously on heterogeneous platforms. To address this need, we propose HiLITE, a hierarchical imitation learning framework that maximizes the energy efficiency while satisfying soft real-time constraints on embedded SoCs. Our approach first trains DPM policies using imitation learning; then, it applies a regression policy at runtime to minimize deadline misses. HiLITE improves the energy-delay product by 40 percent on average, and reduces deadline misses by up to 76 percent, compared to state-of-the-art approaches. In addition, we show that the trained policies not only achieve high accuracy, but also have negligible prediction time overhead and small memory footprint.