Vertical federated learning trains models from feature-partitioned datasets across multiple clients, who collaborate without sharing their local data. Standard approaches assume that all feature partitions are available during both training and inference. Yet, in practice, this assumption rarely holds, as for many samples only a subset of the clients observe their partition. However, not utilizing incomplete samples during training harms generalization, and not supporting them during inference limits the utility of the model. Moreover, if any client leaves the federation after training, its partition becomes unavailable, rendering the learned model unusable. Missing feature blocks are therefore a key challenge limiting the applicability of vertical federated learning in real-world scenarios. To address this, we propose LASER-VFL, a vertical federated learning method for efficient training and inference of split neural network-based models that is capable of handling arbitrary sets of partitions. Our approach is simple yet effective, relying on the strategic sharing of model parameters and on task-sampling to train a family of predictors. We show that LASER-VFL achieves a $\mathcal{O}({1}/{\sqrt{T}})$ convergence rate for nonconvex objectives in general, $\mathcal{O}({1}/{T})$ for sufficiently large batch sizes, and linear convergence under the Polyak-{\L}ojasiewicz inequality. Numerical experiments show improved performance of LASER-VFL over the baselines. Remarkably, this is the case even in the absence of missing features. For example, for CIFAR-100, we see an improvement in accuracy of $21.4\%$ when each of four feature blocks is observed with a probability of 0.5 and of $12.2\%$ when all features are observed.

翻译：纵向联邦学习利用多个客户端间特征划分的数据集训练模型，各客户端在不共享本地数据的前提下进行协作。标准方法假设所有特征划分在训练和推理阶段均可用。然而在实践中，该假设极少成立，因为对于多数样本而言，仅有部分客户端能观测到其对应的特征划分。若在训练中舍弃不完整样本会损害模型泛化能力，而在推理阶段不支持此类样本则会限制模型实用性。此外，若任意客户端在训练后退出联邦，其对应的特征划分将不可用，导致已训练模型失效。因此，特征块缺失是限制纵向联邦学习在实际场景中应用的关键挑战。为解决该问题，我们提出LASER-VFL——一种面向基于拆分神经网络模型高效训练与推理的纵向联邦学习方法，该方法能够处理任意划分组合。我们的方案简洁高效，通过策略性共享模型参数并结合任务采样技术来训练预测器族。理论分析表明：LASER-VFL在非凸目标下具有$\mathcal{O}({1}/{\sqrt{T}})$的收敛速率，在足够大的批次规模下可达$\mathcal{O}({1}/{T})$，并在满足Polyak-{\L}ojasiewicz不等式时实现线性收敛。数值实验显示LASER-VFL在各项基准测试中均取得性能提升。值得注意的是，即使在特征完整的情况下该方法仍具优势。以CIFAR-100数据集为例，当四个特征块各自以0.5概率被观测时，准确率提升达$21.4\%$；当所有特征均被观测时，准确率仍提升$12.2\%$。