Federated Logistic Regression

Logistic Regression(LR) is a widely used statistic model for classification problems. FATE provided two modes of federated LR: Homogeneous LR (HomoLR) and Heterogeneous LR (HeteroLR and Hetero_SSHE_LR).

Below lists features of each LR models:

Linear Model	Multiclass(OVR)	Arbiter-Less Training	Multi-Host	Cross Validation	Warm-Start
Coordinated LR	✓	✗	✓	✓	✓
SSHE LR	✓	✓	✗	✓	✓
Homo LR	✓	✗	✓	✓	✓

We simplified the federation process into three parties. Party A represents Guest， party B represents Host while party C, which also known as "Arbiter", is a third party that holds a private key for each party and work as a coordinator.

Coordinated LR

The CoordinatedLR carries out the federated learning in a different way. As shown in Figure 2, A sample alignment process is conducted before training. This sample alignment process is to identify overlapping samples stored in databases of the two involved parties. The federated model is built based on those overlapping samples. The whole sample alignment process will not leak confidential information (e.g., sample ids) on the two parties since it is conducted in an encrypted way. (Security of this algorithm is lower than SSHE-LR, use SSHE-LR if possible)

In the training process, party A and party B compute out the elements needed for final gradients. Arbiter aggregate them and compute out the gradient and then transfer back to each party. More details is available in this: Private federated learning on vertically partitioned data via entity resolution and additively homomorphic encryption.

Multi-host hetero-lr

For multi-host scenario, the gradient computation still keep the same as single-host case. However, we use the second-norm of the difference of model weights between two consecutive iterations as the convergence criterion. Since the arbiter can obtain the completed model weight, the convergence decision is happening in Arbiter.

Heterogeneous SSHE Logistic Regression

FATE implements a heterogeneous logistic regression without arbiter role called for hetero_sshe_lr. More details is available in this following paper: When Homomorphic Encryption Marries Secret Sharing: Secure Large-Scale Sparse Logistic Regression and Applications in Risk Control. We have also made some optimization so that the code may not exactly same with this paper. The training process could be described as the following: forward and backward process.

The training process is based secure matrix multiplication protocol(SMM), which HE and Secret-Sharing hybrid protocol is included.

Features

• Both Homo-LR and Hetero-LR(CoordinatedLR)

1. L1 & L2 regularization

2. Mini-batch mechanism

3. Weighted training

4. Torch optimization methods:

   > - rmsprop: RMSProp
   >   - adadelta: AdaDelta
   >   - adagrad: AdaGrad
   >   - adam: Adam
   >   - adamw: AdamW
   >   - adamax: Adamax
   >   - asgd: ASGD
   >   - nadam: NAdam
   >   - radam: RAdam
   >   - rprop: RProp
   >   - sgd: gradient descent with arbitrary batch size
   

5. Torch Learning Rate Scheduler methods: > > - constant > > - step > > - linear

6. Three converge criteria:

   > - diff  
          > >     Use difference of loss between two iterations, not available
          > >     for multi-host training;
   >
   >   - abs  
            > >     use the absolute value of loss;
   >
   >   - weight\_diff  
            > >     use difference of model weights
   

7. Support multi-host modeling task.

Hetero-LR extra features

1. When modeling a multi-host task, "weight_diff" converge criteria is supported only.