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# System prepended metadata

title: Research Proposal of Feature Disentanglement in Federated Learning Settings

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# Research Proposal of Feature Disentanglement in Federated Learning Settings

### Introduction

Federated learning is a decentralized learning approach that enables multiple clients to collaboratively learn a machine learning model while keeping the training data on the distributed local devices<sup>[[1]](#1)</sup>. Although federated learning achieves better privacy and efficiency, existing methods neglect the fact that the data on each node are collected in a non-iid manner, resulting in the domain shift problem<sup>[[2]](#2)</sup>. Specifically, the models trained within federated networks might fail to generalize to new devices since the data distribution of source nodes may statistically differ from the target nodes' unlabeled data. Fortunately, Unsupervised Domain Adaptation (UDA) has significantly unravelled the predicament prompted by out-of-distributed data (OOD). Nonetheless, the existing methods simply assume the data are centralized on one server, suffocating their applicability to the federated learning systems<sup>[[3]](#3)[[4]](#4)[[5]](#5)[[6]](#6)[[7]](#7)[[8]](#8)[[9]](#9)[[10]](#10)</sup>. Therefore, a novel federated learning algorithm with domain adaptation capability has aroused our research interest.

### Proposed Methods

Here we have proposed the following research ideas regarding domain adapration in federated learning settings.

**(1) Federated Learning Domain Adaptation using Domain-invariant Features**

We have proposed an approach to perform federated learning domain adaptation using domain-invariant features. 

Let us assume that we have *N* clients in the federated learning network <img src="https://latex.codecogs.com/gif.latex?D&space;=&space;\{{D_k}\}_{k=1}^N" title="D = \{{D_{k}}\}_{k=1}^N" /> 

In our approach, the **Feature Disentangler** will disentangle the local features into (i) domain-specific feature, (ii) domain-invariant feature, and (iii) random feature. 

Suppose the extracted domain-invariant feature denotes as <img src="https://latex.codecogs.com/gif.latex?R&space;=&space;\{{R_{k}}\}_{k=1}^N" title="R = \{{R_{k}}\}_{k=1}^N" />

Then we may calculate *R* using Feature Disentangler *P*: <img src="https://latex.codecogs.com/gif.latex?{R_{k}}&space;=&space;P_{k}(D_{k})" title="{R_{k}} = P_{k}(D_{k})" />

The representation disentanglement will exceedingly mitigate the domain shift problem induced by out-of-distributed data (OOD) and ameliorate downstream federated learning tasks' training efficiency. 

Then, each node's local model will train the domain-invariant feature, and their gradients are aggregated to update the global target model. In particular, the goal is to minimize the following objective function.

<img src="https://latex.codecogs.com/gif.latex?\min_{w}&space;f(w)&space;=&space;\sum_{k=1}^{N}&space;p_{k}&space;F_{k}(w)" title="\min_{w} f(w) = \sum_{k=1}^{N} p_{k} F_{k}(w)" style="display: block; margin-left: auto; margin-right: auto; width: 50%; max-width: 180px"/>

Here <img src="https://latex.codecogs.com/gif.latex?p_{k}&space;\geq&space;0" title="p_{k} \geq 0" /> and <img src="https://latex.codecogs.com/gif.latex?\sum\nolimits_{k=1}^{N}&space;p_{k}&space;=&space;1" title="\sum\nolimits_{k=1}^{N} p_{k} = 1" />

The local objective function *F<sub>k</sub>* is often defined as the empirical risk over local data: 

<img src="https://latex.codecogs.com/gif.latex?F_{k}(w)&space;=&space;\frac{1}{n_k}&space;\sum_{j_{k}&space;=&space;1}^{n_k}&space;L(R_{j_{k}};&space;w)" title="F_{k}(w) = \frac{1}{n_k} \sum_{j_{k} = 1}^{n_k} L(R_{j_{k}}; w)" style="display: block; margin-left: auto; margin-right: auto; width: 50%; max-width: 180px"/>

The approach has been demonstrated in Figure 1.

![domain_invariant](https://i.imgur.com/ytbdStn.png)

*Figure 1.* Federated Learning Domain Adaptation using Domain-invariant Features

**(2) Federated Learning Domain-specific Feature Modeling**

Furthermore, in addition to modeling domain-invariant features, our approach may also find latent distribution with domain-specific feature in federated learning settings. 

Suppose the extracted domain-specific feature denotes as <img src="https://latex.codecogs.com/gif.latex?S&space;=&space;\{{S_{k}}\}_{k=1}^N" title="S = \{{S_{k}}\}_{k=1}^N" />

Then we may calculate *S* using Feature Disentangler *P*: <img src="https://latex.codecogs.com/gif.latex?{S_{k}}&space;=&space;P_{k}(D_{k})" title="{S_{k}} = P_{k}(D_{k})" />

The local model will seperately train the domain-specific feature of each node. Meanwhile, their gradients are aggregated to update the global target model using federated learning algorithm.

The local objective function of federated learning *F<sub>k</sub>* is defined as follows: 

<img src="https://latex.codecogs.com/gif.latex?F_{k}(w)&space;=&space;\frac{1}{n_k}&space;\sum_{j_{k}&space;=&space;1}^{n_k}&space;L(S_{j_{k}};&space;w)" title="F_{k}(w) = \frac{1}{n_k} \sum_{j_{k} = 1}^{n_k} L(S_{j_{k}}; w)" style="display: block; margin-left: auto; margin-right: auto; width: 50%; max-width: 180px"/>

The approach has been demonstrated in Figure 2.

![domain_specific](https://i.imgur.com/1eVuz6p.png)

### Reference

<a name="1"></a>[1. Communication-Efficient Learning of Deep Networks from Decentralized Data](https://arxiv.org/abs/1602.05629)

<a name="2"></a>[2. Dataset Shift in Machine Learning](http://www.acad.bg/ebook/ml/The.MIT.Press.Dataset.Shift.in.Machine.Learning.Feb.2009.eBook-DDU.pdf)

<a name="3"></a>[3. Unsupervised domain adaptation by backpropagation](https://arxiv.org/abs/1409.7495)

<a name="4"></a>[4. Adversarial discriminative domain adaptation](https://arxiv.org/abs/1702.05464)

<a name="5"></a>[5. A theory of learning from different domains](https://www.alexkulesza.com/pubs/adapt_mlj10.pdf)

<a name="6"></a>[6. Beyond Sharing Weights for Deep Domain Adaptation](https://arxiv.org/pdf/1603.06432.pdf)

<a name="7"></a>[7. Coupled Generative Adversarial Networks](https://arxiv.org/abs/1606.07536)

<a name="8"></a>[8. Pixel-Level Domain Transfer](https://arxiv.org/abs/1603.07442)

<a name="9"></a>[9. Domain-Adversarial Training of Neural Networks](https://arxiv.org/abs/1505.07818)

<a name="10"></a>[10. Deep Reconstruction-Classification Networks for Unsupervised Domain Adaptation](https://arxiv.org/abs/1607.03516)



