Ubiquitous mobile devices have catalyzed the development of vehicle crowd sensing (VCS). In particular, vehicle sensing systems show great potential in the flexible acquisition of spatio-temporal urban data through built-in sensors under diverse sensing scenarios. However, vehicle systems often exhibit biased coverage due to the heterogeneous nature of trip requests and routes. To achieve a high sensing coverage, a critical challenge lies in optimally relocating vehicles to minimize the divergence between vehicle distributions and target sensing distributions. Conventional approaches typically employ a two-stage predict-then-optimize (PTO) process: first predicting real-time vehicle distributions and subsequently generating an optimal relocation strategy based on the predictions. However, this approach can lead to suboptimal decision-making due to the propagation of errors from upstream prediction. To this end, we develop an end-to-end Smart Predict-then-Optimize (SPO) framework by integrating optimization into prediction within the deep learning architecture, and the entire framework is trained by minimizing the task-specific matching divergence rather than the upstream prediction error. Methodologically, we formulate the vehicle relocation problem by quadratic programming (QP) and incorporate a novel unrolling approach based on the Alternating Direction Method of Multipliers (ADMM) within the SPO framework to compute gradients of the QP layer, facilitating backpropagation and gradient-based optimization for end-to-end learning. The effectiveness of the proposed framework is validated by real-world taxi datasets in Hong Kong. Utilizing the alternating differentiation method, the general SPO framework presents a novel concept of addressing decision-making problems with uncertainty, demonstrating significant potential for advancing applications in intelligent transportation systems.

Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is to predict, then optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in a downstream optimization problem. In contrast, we propose a new and very general framework, called Smart "Predict, then Optimize" (SPO), which directly leverages the optimization problem structure, i.e., its objective and constraints, for designing successful analytics tools. A key component of our framework is the SPO loss function, which measures the quality of a prediction by comparing the objective values of the solutions generated using the predicted and observed parameters, respectively. Training a model with respect to the SPO loss is computationally challenging, and therefore we also develop a surrogate loss function, called the SPO+ loss, which upper bounds the SPO loss, has desirable convexity properties, and is statistically consistent under mild conditions. We also propose a stochastic gradient descent algorithm which allows for situations in which the number of training samples is large, model regularization is desired, and/or the optimization problem of interest is nonlinear or integer. Finally, we perform computational experiments to empirically verify the success of our SPO framework in comparison to the standard predict-then-optimize approach.