Vertical federated learning

Overview

In vertical federated learning (VFL) several parties hold different features of the same set of users, and one of them, the active party, also holds the labels. They want one joint model without exposing raw data or local model parameters 2211.12814 §2.1. Each party keeps its feature block and its local model. During training the parties exchange intermediate outputs and gradients rather than raw features 2211.12814 §2.2. This differs from horizontal FL, where parties share a feature space and differ in samples 2211.12814 tab. 1. The survey also shows that these exchanged results can leak information through label inference, feature inference and backdoor attacks 2211.12814 §5.3.1 2211.12814 §5.3.2 2211.12814 §5.4.

A general federated learning survey lists VFL as one of its FL types. Its example is two organisations that hold different feature sets for the same people 2101.05428 §3. That survey does not give a protocol for VFL, so the training details on this page come from the VFL survey.

The word "vertical" also appears in federated reinforcement learning, where it names a different setting: agents share one environment and each sees only part of its state 2108.11887 §4.3. That is not a split of features among parties, so the VFL rules on this page do not apply to it. It is covered under Variants. The same FRL survey lists VFL as one of three federated learning categories by data partition 2108.11887 §2.3.

Variants

Split VFL (splitVFL)

The active party keeps a trainable global module that takes the concatenated local outputs. Local models can be neural networks, linear or logistic regression, SVMs, K-means or EM models 2211.12814 §2.1. Card: Vertical Federated Learning: Concepts, Advances and Challenges.

Aggregation VFL (aggVFL)

The top step is a fixed function rather than a trained module. The card names a sigmoid and an optimal split search for trees as examples [arxiv:2211.12814 §2.1] 2211.12814 tab. 2. Card: Vertical Federated Learning: Concepts, Advances and Challenges.

Variants without active-party features (splitVFL_c, aggVFL_c)

The active party holds the labels but no features of its own, and the same two top-step choices apply 2211.12814 §2.1 2211.12814 tab. 2. Card: Vertical Federated Learning: Concepts, Advances and Challenges.

Federated transfer learning (FTL)

The general FL survey describes federated transfer learning as the extension of VFL to sample instances that not every organisation holds 2101.05428 §3. The VFL survey's protocol works on N aligned samples, with IDs matched by private set intersection 2211.12814 §2.1 2211.12814 §2.2. FTL therefore relaxes that assumption. The general survey gives no protocol for it, so none of the rows above can be carried over unchanged. Card: Federated Learning: Opportunities and Challenges.

Tree-based VFL

Each party holds part of each tree, and the parts together form one tree. The active party gathers the split information it receives and picks the best split 2211.12814 §2.2.1. GBDT methods such as SecureBoost use additive homomorphic encryption on gradients and histograms. Random-forest variants use bagging, with encryption or a third party 2211.12814 §2.2.1. Card: Vertical Federated Learning: Concepts, Advances and Challenges.

Communication-efficient methods

The survey groups five families: several local updates per round (FedBCD and others), asynchronous coordination, one-shot communication, compression of transmitted data, and selection of samples or features [arxiv:2211.12814 §3.1–§3.5]. Card: Vertical Federated Learning: Concepts, Advances and Challenges.

Effectiveness methods for scarce labels

Self-supervised, semi-supervised, knowledge-distillation and transfer-learning approaches help when labels are few or a party holds little data [arxiv:2211.12814 §4.1–§4.4]. Card: Vertical Federated Learning: Concepts, Advances and Challenges.

Privacy defenses

Cryptographic defenses wrap the transmitted outputs and gradients, using homomorphic encryption, secure multi-party computation or a trusted execution environment 2211.12814 §2.2 2211.12814 §5.3.3. Non-cryptographic defenses add noise, discretise gradients or sparsify them; the survey notes these trade utility for privacy 2211.12814 §5.3.4. Card: Vertical Federated Learning: Concepts, Advances and Challenges.

Library support (FedML)

FedML is an open research library. Its worker-oriented message API and topology manager list vertical FL among the topologies it supports, next to split learning, decentralized FL and hierarchical FL 2007.13518 §3. The paper says the library ships a reference implementation of vertical FL 2007.13518 §4.1. Its reported experiments cover FedAvg only 2007.13518 §5 2007.13518 tab. 5. Card: FedML: A Research Library and Benchmark for Federated Machine Learning.

Vertical federated reinforcement learning (VFRL)

This is not feature-partitioned VFL. All agents act in one shared environment, but each observes only part of the state, so their observation spaces differ and together cover the global state 2108.11887 §4.3. Decision-oriented agents act and receive rewards; support-oriented agents only observe 2108.11887 §4.3. The card's six-step procedure initialises the models, collects state-action-reward-state tuples, sends encrypted intermediate products to a federated model, aggregates them, sends encrypted parameters back, and updates each local model 2108.11887 §4.3 steps 1-6. Card: Federated Reinforcement Learning: Techniques, Applications, and Open Challenges.

When to use which

The surveys report no experiments, so none of these rows is a measured ranking. Treat them as a design checklist. The VFLow framework frames the choice as a constrained trade-off between task loss, privacy, efficiency and bias, but gives no values or measures for its bounds 2211.12814 §7.

Implementation sketch

The sketch shows the split VFL loop 2211.12814 alg. 1. For aggVFL, replace top_model with a fixed function and skip its update. Tree-based VFL does not use this loop; it exchanges split information instead 2211.12814 §2.2.1. The survey says encryption, secure multi-party computation or a trusted execution environment can wrap the transmitted values 2211.12814 §2.2; the sketch leaves them out.

# One VFL mini-batch, split form  [arxiv:2211.12814 alg. 1]
# Inputs: eta_1 (active party's top module), eta_2 (local models)

def vfl_step(batch_ids, features, labels, local_models, top_model):
    # Each party k computes its local output H_k on the batch  [arxiv:2211.12814 alg. 1]
    outputs = [
        local_models[k](features[k][batch_ids])  # H_k, size not stated
        for k in range(num_parties)
    ]
    # Active party: loss on the joined outputs, then update top module
    loss = task_loss(top_model(outputs), labels[batch_ids])
    top_model.update(eta_1 * grad(loss, top_model.params))
    # Active party sends dloss/dH_k back to party k  [arxiv:2211.12814 alg. 1]
    output_grads = grad(loss, outputs)
    # Party k turns its output gradient into a parameter update  [arxiv:2211.12814 eq. 3]
    for k in range(num_parties):
        local_models[k].update(eta_2 * local_grad(output_grads[k]))
    return loss

Two points the paper leaves for the implementer. The algorithm sends the output gradients without encryption, while the encrypted exchange is described only in prose 2211.12814 alg. 1 2211.12814 §2.2. Its notation drifts between indices i and k in §2.2 and between 2211.12814 eq. 3 and 2211.12814 alg. 1; read each party's output as one tensor per mini-batch 2211.12814 §2.2.

Contradictions

None known. The VFL claims rest on one survey, so there is no second source on the same setting to disagree with. The federated RL survey uses "vertical" for a different setting, so its results do not bear on the VFL rows above and no conflict is recorded. The general FL survey's one-line description of FTL is not checked against any second source; the VFL survey does not cover FTL.

Papers

• Vertical Federated Learning: Concepts, Advances and Challenges: survey of VFL covering the training protocol, communication, privacy attacks and defenses, fairness, applications and open challenges, plus the VFLow design framework. No experiments and no official code.
• Federated Learning: Opportunities and Challenges: general FL survey with a short taxonomy that names VFL and federated transfer learning, plus training bottlenecks, attacks and defences. The survey has no experiments and no official code.
• Federated Reinforcement Learning: Techniques, Applications, and Open Challenges: survey of federated RL, with a "vertical" setting in which agents share one environment and each sees part of its state. This is not feature-partitioned VFL. The survey has no experiments of its own.
• FedML: A Research Library and Benchmark for Federated Machine Learning: open library and benchmark for FL research, whose worker API can express vertical FL topologies. Its reported experiments use FedAvg only. Official code (Apache-2.0).