Vertical federated learning is a collaborative machine learning framework to train deep leaning models on vertically partitioned data with privacy-preservation. It attracts much attention both from academia and industry. Unfortunately, applying most existing vertical federated learning methods in real-world applications still faces two daunting challenges. First, most existing vertical federated learning methods have a strong assumption that at least one party holds the complete set of labels of all data samples, while this assumption is not satisfied in many practical scenarios, where labels are horizontally partitioned and the parties only hold partial labels. Existing vertical federated learning methods can only utilize partial labels, which may lead to inadequate model update in end-to-end backpropagation. Second, computational and communication resources vary in parties. Some parties with limited computational and communication resources will become the stragglers and slow down the convergence of training. Such straggler problem will be exaggerated in the scenarios of horizontally partitioned labels in vertical federated learning. To address these challenges, we propose a novel vertical federated learning framework named Cascade Vertical Federated Learning (CVFL) to fully utilize all horizontally partitioned labels to train neural networks with privacy-preservation. To mitigate the straggler problem, we design a novel optimization objective which can increase stragglers contribution to the trained models. We conduct a series of qualitative experiments to rigorously verify the effectiveness of CVFL. It is demonstrated that CVFL can achieve comparable performance (e.g., accuracy for classification tasks) with centralized training. The new optimization objective can further mitigate the straggler problem comparing with only using the asynchronous aggregation mechanism during training.
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