Federated Adversarial Domain Adaptation

Federated learning improves data privacy and efficiency in machine learning performed over networks of distributed devices , such as mobile phones , IoT and wearable devices , etc . Yet models trained with federated learning can still fail to generalize to new devices due to the problem of domain shift . Domain shift occurs when the labeled data collected by source nodes statistically differs from the target node ’ s unlabeled data . In this work , we present a principled approach to the problem of federated domain adaptation , which aims to align the representations learned among the different nodes with the data distribution of the target node . Our approach extends adversarial adaptation techniques to the constraints of the federated setting . In addition , we devise a dynamic attention mechanism and leverage feature disentanglement to enhance knowledge transfer . Empirically , we perform extensive experiments on several image and text classification tasks and show promising results under unsupervised federated domain adaptation setting . 1 INTRODUCTION . Data generated by networks of mobile and IoT devices poses unique challenges for training machine learning models . Due to the growing storage/computational power of these devices and concerns about data privacy , it is increasingly attractive to keep data and computation locally on the device ( Smith et al. , 2017 ) . Federated Learning ( FL ) ( Mohassel & Rindal , 2018 ; Bonawitz et al. , 2017 ; Mohassel & Zhang , 2017 ) provides a privacy-preserving mechanism to leverage such decen-tralized data and computation resources to train machine learning models . The main idea behind federated learning is to have each node learn on its own local data and not share either the data or the model parameters . While federated learning promises better privacy and efficiency , existing methods ignore the fact that the data on each node are collected in a non-i.i.d manner , leading to domain shift between nodes ( Quionero-Candela et al. , 2009 ) . For example , one device may take photos mostly indoors , while another mostly outdoors . In this paper , we address the problem of transferring knowledge from the decentralized nodes to a new node with a different data domain , without requiring any additional supervision from the user . We define this novel problem Unsupervised Federated Domain Adaptation ( UFDA ) , as illustrated in Figure 1 ( a ) . There is a large body of existing work on unsupervised domain adaptation ( Long et al. , 2015 ; Ganin & Lempitsky , 2015 ; Tzeng et al. , 2017 ; Zhu et al. , 2017 ; Gong et al. , 2012 ; Long et al. , 2018 ) , but the federated setting presents several additional challenges . First , the data are stored locally and can not be shared , which hampers mainstream domain adaptation methods as they need to access both the labeled source and unlabeled target data ( Tzeng et al. , 2014 ; Long et al. , 2017 ; Ghifary et al. , 2016 ; Sun & Saenko , 2016 ; Ganin & Lempitsky , 2015 ; Tzeng et al. , 2017 ) . Second , the model parameters are trained separately for each node and converge at different speeds , while also offering different contributions to the target node depending on how close the two domains are . Finally , the knowledge learned from source nodes is highly entangled ( Bengio et al. , 2013 ) , which can possibly lead to negative transfer ( Pan & Yang , 2010 ) . In this paper , we propose a solution to the above problems called Federated Adversarial Domain Adaptation ( FADA ) which aims to tackle domain shift in a federated learning system through adversarial techniques . Our approach preserves data privacy by training one model per source node and updating the target model with the aggregation of source gradients , but does so in a way that reduces domain shift . First , we analyze the federated domain adaptation problem from a theoretical perspective and provide a generalization bound . Inspired by our theoretical results , we propose an efficient adaptation algorithm based on adversarial adaptation and representation disentanglement applied to the federated setting . We also devise a dynamic attention model to cope with the varying convergence rates in the federated learning system . We conduct extensive experiments on real-world datasets , including image recognition and natural language tasks . Compared to baseline methods , we improve adaptation performance on all tasks , demonstrating the effectiveness of our devised model . 2 RELATED WORK . Unsupervised Domain Adaptation Unsupervised Domain Adaptation ( UDA ) aims to transfer the knowledge learned from a labeled source domain to an unlabeled target domain . Domain adaptation approaches proposed over the past decade include discrepancy-based methods ( Tzeng et al. , 2014 ; Long et al. , 2017 ; Ghifary et al. , 2014 ; Sun & Saenko , 2016 ; Peng & Saenko , 2018 ) , reconstructionbased UDA models ( Yi et al. , 2017 ; Zhu et al. , 2017 ; Hoffman et al. , 2018 ; Kim et al. , 2017 ) , and adversary-based approaches ( Liu & Tuzel , 2016 ; Tzeng et al. , 2017 ; Liu et al. , 2018a ; Ganin & Lempitsky , 2015 ) . For example , Ganin & Lempitsky ( 2015 ) propose a gradient reversal layer to perform adversarial training to a domain discriminator , inspired by the idea of adversarial learning . Tzeng et al . ( 2017 ) address unsupervised domain adaptation by adapting a deep CNN-based feature extractor/classifier across source and target domains via adversarial training . Ben-David et al . ( 2010 ) introduce anH∆H-divergence to evaluate the domain shift and provide a generalization error bound for domain adaptation . These methods assume the data are centralized on one server , limiting their applicability to the distributed learning system . Federated Learning Federated learning ( Mohassel & Rindal , 2018 ; Rivest et al. , 1978 ; Bonawitz et al. , 2017 ; Mohassel & Zhang , 2017 ) is a decentralized learning approach which enables multiple clients to collaboratively learn a machine learning model while keeping the training data and model parameters on local devices . Inspired by Homomorphic Encryption ( Rivest et al. , 1978 ) , GiladBachrach et al . ( 2016 ) propose CryptoNets to enhance the efficiency of data encryption , achieving higher federated learning performance . Bonawitz et al . ( 2017 ) introduce a secure aggregation scheme to update the machine learning models under their federated learning framework . Recently , Mohassel & Zhang ( 2017 ) propose SecureML to support privacy-preserving collaborative training in a multiclient federated learning system . However , these methods mainly aim to learn a single global model across the data and have no convergence guarantee , which limits their ability to deal with non-i.i.d . data . To address the non-i.i.d data , Smith et al . ( 2017 ) introduce federated multi-task learning , which learns a separate model for each node . Liu et al . ( 2018b ) propose semi-supervised federated transfer learning in a privacy-preserving setting . However , their models involve full or semi-supervision . The work proposed here is , to our best knowledge , the first federated learning framework to consider unsupervised domain adaptation . Feature Disentanglement Deep neural networks are known to extract features where multiple hidden factors are highly entangled . Learning disentangled representations can help remove irrelevant and domain-specific features and model only the relevant factors of data variation . To this end , recent work ( Mathieu et al. , 2016 ; Makhzani et al. , 2016 ; Liu et al. , 2018a ; Odena et al. , 2017 ) explores the learning of interpretable representations using generative adversarial networks ( GANs ) ( Goodfellow et al. , 2014 ) and variational autoencoders ( VAEs ) ( Kingma & Welling , 2013 ) . Under the fully supervised setting , ( Odena et al. , 2017 ) propose an auxiliary classifier GAN ( AC-GAN ) to achieve representation disentanglement . ( Liu et al. , 2018a ) introduce a unified feature disentanglement framework to learn domain-invariant features from data across different domains . ( Kingma et al. , 2014 ) also extend VAEs into the semi-supervised setting for representation disentanglement . ( Lee et al. , 2018 ) propose to disentangle the features into a domain-invariant content space and a domainspecific attributes space , producing diverse outputs without paired training data . Inspired by these works , we propose a method to disentangle the domain-invariant features from domain-specific features , using an adversarial training process . In addition , we propose to minimize the mutual information between the domain-invariant features and domain-specific features to enhance the feature disentanglement . 3 GENERALIZATION BOUND FOR FEDERATED DOMAIN ADAPTATION . We first define the notation and review a typical theoretical error bound for single-source domain adaptation ( Ben-David et al. , 2007 ; Blitzer et al. , 2008 ) devised by Ben-David et al . Then we describe our derived error bound for unsupervised federated domain adaptation . We mainly focus on the high-level interpretation of the error bound here and refer our readers to the appendix ( see supplementary material ) for proof details . Notation . LetDS1 andDT denote source and target distribution on input space X and a ground-truth labeling function g : X → { 0 , 1 } . A hypothesis is a function h : X → { 0 , 1 } with the error w.r.t the ground-truth labeling function g : S ( h , g ) : = Ex∼DS [ |h ( x ) − g ( x ) | ] . We denote the risk and empirical risk of hypothesis h on DS as S ( h ) and ̂S ( h ) . Similarly , the risk and empirical risk of h on DT are denoted as T ( h ) and ̂T ( h ) . The H-divergence between two distributions D and D′ is defined as : dH ( D , D′ ) : = 2 supA∈AH |PrD ( A ) − PrD′ ( A ) | , whereH is a hypothesis class for input space X , and AH denotes the collection of subsets of X that are the support of some hypothesis inH . The symmetric difference spaceH∆H is defined as : H∆H : = { h ( x ) ⊕ h′ ( x ) ) |h , h′ ∈ H } , ( ⊕ : the XOR operation ) . We denote the optimal hypothesis that achieves the minimum risk on the source and the target as h∗ : = arg minh∈H S ( h ) + T ( h ) and the error of h∗ as λ : = S ( h∗ ) + T ( h∗ ) . Blitzer et al . ( 2007b ) prove the following error bound on the target domain . Theorem 1 . LetH be a hypothesis space of V C-dimension d and D̂S , D̂T be the empirical distribution induced by samples of size m drawn from DS and DT . Then with probability at least 1− δ over the choice of samples , for each h ∈ H , T ( h ) ≤ ̂S ( h ) + 1 2 d̂H∆H ( D̂S , D̂T ) + 4 √ 2d log ( 2m ) + log ( 4/δ ) m + λ ( 1 ) Let DS= { DSi } Ni=1 , and DT = { xtj } nt j=1 be N source domains and the target domain in a UFDA system , where DSi = { ( xsj , ysj ) } ni j=1 . In federated domain adaptation system , DS is distributed on N nodes and the data are not shareable with each other in the training process . The classical domain adaptation algorithms aim to minimize the target risk T ( h ) : = Pr ( x , y ) ∼DT [ h ( x ) 6= y ] . However , in a UFDA system , one model can not directly get access to data stored on different nodes for security and privacy reasons . To address this issue , we propose to learn separate models for each distributed source domain hS = { hSi } Ni=1 . The target hypothesis hT is the aggregation of the parameters of hS , i.e . hT : = ∑N i=1 αihSi , ∀α ∈ RN+ , ∑ i∈ [ N ] αi = 1 . We can then derive the following error bound : Theorem 2 . ( Weighted error bound for federated domain adaptation ) . LetH be a hypothesis class with VC-dimension d and { D̂Si } Ni=1 , D̂T be empirical distributions induced by a sample of size 1In this literature , the calligraphic D denotes data distribution , and italic D denotes domain discriminator . m from each source domain and target domain in a federated learning system , respectively . Then , ∀α ∈ RN+ , ∑N i=1 αi = 1 , with probability at least 1− δ over the choice of samples , for each h ∈ H , T ( hT ) ≤ ̂S̃ ( ∑ i∈ [ N ] αihSi ) ︸ ︷︷ ︸ error on source + ∑ i∈ [ N ] αi ( 1 2 d̂H∆H ( D̂Si , D̂T ) ︸ ︷︷ ︸ ( DSi , DT ) divergence +λi ) + 4 √ 2d log ( 2Nm ) + log ( 4/δ ) Nm︸ ︷︷ ︸ VC-Dimension Constraint ( 2 ) where λi is the risk of the optimal hypothesis on the mixture of DSi and T , and S̃ is the mixture of source samples with size Nm . d̂H∆H ( D̂Si , D̂T ) denotes the divergence between domain Si and T . Comparison with Existing Bounds The bound in ( 2 ) is extended from ( 1 ) and they are equivalent if only one source domain exists ( N = 1 ) . Mansour et al . ( 2009 ) provide a generalization bound for multiple-source domain adaptation , assuming that the target domain is a mixture of the N source domains . In contrast , in our error bound ( 2 ) , the target domain is assumed to be an novel domain , resulting in a bound involvingH∆H discrepancy ( Ben-David et al. , 2010 ) and the VC-dimensional constraint ( Vapnik & Vapnik , 1998 ) . Blitzer et al . ( 2007b ) propose a generalization bound for semisupervised multi-source domain adaptation , assuming that partial target labels are available . Our generalization bound is devised for unsupervised learning . Zhao et al . ( 2018 ) introduce classification and regression error bounds for multi-source domain adaptation . However , these error bounds assume that the multiple source and target domains exactly share the same hypothesis . In contrast , our error bound involves multiple hypotheses .

Summary: This paper introduces an unsupervised federated domain adaptation (UFDA) problem and proposes a new model called Federated Adversarial Domain Adaptation (FADA) to transfer the knowledge learned from distributed source domains to an unlabeled target domain. This paper uses a dynamic attention mechanism by leveraging the gap statistics to transfer distributed source knowledge. This paper also proposes a method to disentangle the domain-invariant features from domain-specific features, using adversarial training. Moreover, a theoretical generalization bound for UFDA is derived. An extensive empirical evaluation is performed on UFDA vision and linguistic benchmarks.