In a ride-hailing system, an optimal relocation of vacant vehicles can significantly reduce fleet idling time and balance the supply-demand distribution, enhancing system efficiency and promoting driver satisfaction and retention. Model-free deep reinforcement learning (DRL) has been shown to dynamically learn the relocating policy by actively interacting with the intrinsic dynamics in large-scale ride-hailing systems. However, the issues of sparse reward signals and unbalanced demand and supply distribution place critical barriers in developing effective DRL models. Conventional exploration strategy (e.g., the $epsilon$-greedy) may barely work under such an environment because of dithering in low-demand regions distant from high-revenue regions. This study proposes the deep relocating option policy (DROP) that supervises vehicle agents to escape from oversupply areas and effectively relocate to potentially underserved areas. We propose to learn the Laplacian embedding of a time-expanded relocation graph, as an approximation representation of the system relocation policy. The embedding generates task-agnostic signals, which in combination with task-dependent signals, constitute the pseudo-reward function for generating DROPs. We present a hierarchical learning framework that trains a high-level relocation policy and a set of low-level DROPs. The effectiveness of our approach is demonstrated using a custom-built high-fidelity simulator with real-world trip record data. We report that DROP significantly improves baseline models with 15.7% more hourly revenue and can effectively resolve the dithering issue in low-demand areas.
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