Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation

We investigate the control and optimization of vertical federated learning (VFL), a class of distributed machine learning (ML) methods in which edge/fog devices contain separate data features, in dynamic edge/fog networks. Owing to heterogeneous data features and hardware across edge/fog networks, devices' contributions to VFL vary substantially, and, moreover, dynamic edge/fog networks can lead to the permanent exit or entry of select data features. In this setting, our proposed methodology, server controlled VFL in dynamic networks (SC-DN), first establishes the existence of a global first-order stationary point for every global round, and then leverages this result to jointly optimize ML model training and resource consumption based on four key control variables: (i) server placement, (ii) device-to-server transmit power, (iii) local device processor frequency, and (iv) local training iterations per global round. The resulting optimization formulation contains coupled variables as well as numerous forms of logarithmic constraints which we show is a mixed-integer signomial program, an NP-hard problem, and for which we develop a general solver. Finally, via experiments on both image and multi-modal datasets, we show that our methodology demonstrates superior classification/regression performance and resource consumption savings than even greedy methodologies.

Federated learning (FL) is an emerging distributed machine learning paradigm that enables local devices to jointly train a global model while keeping data decentralized and private. We propose a variance-reduction based algorithm, VRA-FedSGD, for FL in the presence of heavy-tailed gradient noise and communication noise, where these noises are prevalent in large-scale machine learning over wireless networks and Internet of Things deployments. VRA-FedSGD employs a momentum variance reduction technique together with a nonlinear mapping to mitigate heavy-tailed gradient noise, and uses a variance-reduced aggregation mechanism to suppress heavy-tailed communication noise. In the mean sense, VRA-FedSGD achieves a convergence rate of {\small$\mathcal{O}\left(K^{-(p-1)/(2p-1)}\right)$} for nonconvex objective functions, where $p$ is the tail index of heavy-tailed noise. In the almost sure sense, VRA-FedSGD achieves a convergence rate of $\tilde{\mathcal{O}}\left(K^{-(1-1/(p-ε))}\right)$ for strongly convex objective functions, where $ε$ is an arbitrarily small constant. Simulated experiments on a logistic regression problem with real-world data verify the effectiveness of VRA-FedSGD.

We propose a novel end-to-end privacy-preserving framework, instantiated by three efficient protocols for different deployment scenarios, covering both input and output privacy, for the vertically split scenario in federated learning (FL), where features are split across clients and labels are not shared by all parties. We do so by distributing the role of the aggregator in FL into multiple servers and having them run secure multiparty computation (MPC) protocols to perform model and feature aggregation and apply differential privacy (DP) to the final released model. While a naive solution would have the clients delegating the entirety of training to run in MPC between the servers, our optimized solution, which supports purely global and also global-local models updates with privacy-preserving, drastically reduces the amount of computation and communication performed using multiparty computation. The experimental results also show the effectiveness of our protocols.