# Secure and Efficient Federated Gradient Boosting Decision Trees
## 4 Secure and Efficient FL for GBDTs  
### The SeFB Framework  
Because the GBDTs model is optimized in function space instead of Euclidean space through gradient descent iterative process, the implementation of federated learning setting of GBDTs algorithm is quite different from that of standard paradigm. Because the weights in this model are specific leaves generated from local data, traditional model exchange technology cannot be applied to combine model parameters at the aggregator. That is to say, it is impossible to train independent weak learner models locality on each side and integrate the tree structures generated by them on the aggregator. At present, the frontier research of GBDTs in horizontal federated learning probably follows the following ways. Participants train a decision tree and send it to other participants. Participants who receive the decision tree will update their local gradient and train the next decision tree, which will take turns until the final task is completed. However, the problem of this scheme is that when the local data set of a participant is very skewed, the quality of the trained decision tree is low and more seriously, the low-quality decision tree will affect all subsequent training processes (this process is irreversible, because the subsequent decision tree will depend on the prediction residuals of all previous models). Therefore, the determination of the first decision tree is particularly important. We hope that in the process of building the first tree, we will select the participant with the best quality and distribution of its data set as the builder, and fully absorb the gradient information of other participants to alleviate the influence of the local skewed data set on the decision tree model. In SeFB, we first collect information about similar instances through LSH, and then use gradient aggregation method to build the tree. In addition, in terms of privacy protection, we have not exposed the original data of each data owner. In the process of subsequent update iteration, if the gradients of similar instances need to be obtained from the participants every time, this means that the communication cost is directly related to the number of participants, which is not suitable for the practical application scenarios of large-scale data sets. Therefore, we adopt the master-slave architecture, and the high-performance server is responsible for the global complex operations, such as calculating the weighted gradients and global leaf weights. Participants are responsible for simple operations, such as calculating hash values, building trees and updating models. The calculation burden of participants is reduced, and at the same time, the communication times are reduced. In addition, in terms of accuracy, because the leaf weights are directly related to the output of the model, them contribute more to the improvement of model accuracy. Therefore, we add global leaf weights to the constructed tree to update the model and improve the accuracy of the model. A schematic of the SeFB framework is shown in Figure 3. It includes the builder (B), the data participants (P) and the global server (GS). The builder is one of the data participants and is responsible for building the tree. The global server is responsible for establishing the global hash table and aggregating the local gradients to calculate the global leaf weight. Data participants is responsible for computing the hash values and gradients and sending them to the global server.