MAMO: Memory-Augmented Meta-Optimization for Cold-startRecommendation

Manqing DongUniversity of New South Wales

dongmanqing@gmail.com

Feng YuanUniversity of New South Wales

Sydney, Australia

Lina YaoUniversity of New South Wales

lina.yao@unsw.edu.au

Xiwei XuData 61, CSIROSydney, Australia

Liming ZhuData 61, CSIROSydney, Australia

ABSTRACTA common challenge for most current recommender systems is thecold-start problem. Due to the lack of user-item interactions, thefine-tuned recommender systems are unable to handle situationswith new users or new items. Recently, some works introduce themeta-optimization idea into the recommendation scenarios, i.e. pre-dicting the user preference by only a few of past interacted items.The core idea is learning a global sharing initialization parame-ter for all users and then learning the local parameters for eachuser separately. However, most meta-learning based recommenda-tion approaches adopt model-agnostic meta-learning for parameterinitialization, where the global sharing parameter may lead themodel into local optima for some users. In this paper, we designtwo memory matrices that can store task-specific memories andfeature-specific memories. Specifically, the feature-specific mem-ories are used to guide the model with personalized parameterinitialization, while the task-specific memories are used to guidethe model fast predicting the user preference. And we adopt a meta-optimization approach for optimizing the proposed method. Wetest the model on two widely used recommendation datasets andconsider four cold-start situations. The experimental results showthe effectiveness of the proposed methods.

CCS CONCEPTS• Information systems→ Recommender systems; • Comput-ing methodologies→ Neural networks.

KEYWORDSRecommender systems; Cold-start problem; Meta learning

1 INTRODUCTIONPersonalized recommender systems are playing more and moreimportant roles in web and mobile applications. Despite the successof traditional matrix-factorization based recommendation meth-ods [4] or the most current deep-learning based techniques [33], a

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common challenge for most recommendation methods is the cold-start problem [28]. Because of the lack of user-item interactions,the recommendation approaches that utilize such interactions areunable to handle the situations where new users or items exist,corresponding to the user cold-start and item cold-start problems.

Traditional way to solve the cold start problem is leveragingauxiliary information into the recommender systems, e.g.,content-based recommender systems [21, 27] and cross-domain recom-menders [16, 25]. For example, to address the item cold-start prob-lem, [27] proposes a hybridmodel inwhich item features are learnedfrom the descriptions of items via a stacked denoising autoen-coder and further combined into a collaborative filtering modeltimeSVD++. In [25], the authors propose a cross-domain latent fea-ture mapping model, where the neighborhood-based cross-domainlatent feature mapping method is applied to learn a feature mappingfunction for each cold-start user. However, the major limitation ofsuch approaches is that the learned model may recommend sameitems for users with similar content thereby neglect the personalinterests.

Inspired by recentworks in few-shot learning [26], meta-learning[24] has been introduced into the recommender systems to solvethe cold-start problem, i.e. predicting a user’s preferences by only afew past interacted items. Most of the current meta-learning basedrecommender systems [5, 15, 34] adopt optimization-based algo-rithms such asmodel-agnostic meta-learning (MAML) [11], for theirpromising performance in learning configuration initialization fornew tasks. Generally, the recommendation for a user is regardedas a learning task. The core idea is learning a global parameter toinitialize the parameter of personalized recommender models. Thepersonalized parameter will be locally updated to learn a specificuser’s preference, and the global parameter will be updated by min-imizing the loss over the training tasks among the users. Then, thelearned global parameter is used to guide the model settings fornew users. For example, [15] uses several fully connected neuralnetworks as recommender models. They first learn user and itemembedding from the user and item profiles, and then feed theminto the recommender model to get predictions. They define twogroups of global parameters: parameters in learning embeddingsand parameters in recommender models. They locally update therecommender model for personalized recommendation and globallyupdate the two groups of parameters for the initialization of newusers. [8] also constructs a deep neural net as the recommender

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model. They define a global parameter for initializing the recom-mender model, and then locally updates the model parameter byintroducing update and stop controllers.

The aforementioned approaches have been proven to be promis-ing with regards to applying meta-optimization in the cold-startscenarios and presenting competitive performance in warm-startscenarios. However, they have the following limitations. Most ofthem are build upon MAML algorithm and its variants, which arepowerful to cope with data sparsity, while having a variety of issuessuch as instability, slow convergence, and weak generalization. Inparticular, they often suffer from gradient degradation ending upwith a local optima when handling users who show different gradi-ent descent directions comparing with the majority of users in thetraining set. To address this issue, we propose Memory-AugmentedMeta-Optimization (MAMO) for cold-start recommendation. Indetails, 1) for solving the problem of local optima, we design afeature-specific memory to provide a personalized bias term wheninitializing the model parameters. Specifically, the feature-specificmemory includes two memory matrices: one stores the user pro-file memory to provide retrievable attention values, and the othercaches the fast gradients of the previous training sets to be readaccording to the retrievable attention values. 2)We further designa task-specific memory cube, i.e. user preference memory, to learnto capture the shared potential user preference commonality on dif-ferent items. It is used as fast weights for the recommender modelto alleviate a need for storing copies of neural activity patterns.3) The extensive experiments on two widely used datasets showMAMO performs favorably against the state-of-the-arts. The codeis publicly available for reproduction1.

The rest of the paper is organized as follows.We review proposedapproach in Section 2; Section 3 presents the settings, experimentalresults and analysis of the experiments; we review the related workin Section 4, followed by the conclusion in Section 5.

2 PROPOSED APPROACH2.1 Overview2.1.1 Problem Definition. We consider the recommendation fora user as one task. Given a user u with profile pu and rated itemsISu , where each item i is associated with a description file pi andcorresponding ratings ySu,i , our goal is predicting the rating yQu,iby user u for a new item i ∈ IQu . Here, S stands for the support set,and Q stands for the query set.

2.1.2 Motivation. Most existing meta learning based recommen-dation techniques attempt to learn a meta global parameter ϕ toguide the model initialization Rθ , i.e. θ ← ϕ, where ϕ is learnedacross all the users in training set. It provides a uniform param-eter initialization to govern the trained recommendation modelto predict on new users. The global parameter ϕ works uniformlyacross all users and thus may be inadequate to discern the intrinsicdiscrepancies among a variety of user patterns, resulting in poorgeneralization. Also, the model may tend to be stuck on a localoptimum and encounter gradient degradation. Instead of learning a

1https://github.com/dongmanqing/Code-for-MAMO

User u

Support Set Query Set

 Item 1 

ProfileMemory MP

 Item 2   Item i 

yu,1 yu,2 yu,iLrec Lrec Lrec

eu

e1 e2 ei

Localupdate

Globalupdate

Task-specificMemory MUI

Recommender

pu

au

User Memory MU

Feature-specific Memory

Figure 1: The training phase of MAMO

single initialization of the model parameters, we propose an adap-tive meta learning recommendation model, Memory-AugmentedMeta-Optimization (MAMO), to improve the stability, generaliza-tion and computational cost of model by learning a multi-levelpersonalized model parameters.

2.1.3 Model Structure. The proposed model includes two parts:the recommender model for predicting the user preference andthe memory-augmented meta-optimization learner for initializ-ing recommender model parameters. The recommender modelRΘ(pu ,pi ) predicts the recommendation scores, where the modelparameters Θ = {θu ,θi ,θr } will be locally updated for singleusers to provide personalized recommendation. The meta-learner,which includes global parameters Φ = {ϕu ,ϕi ,ϕr } and memoriesM = {MU ,MP ,MU , I }, will provide personalized initialization forthe recommender model parameters Θ, and will be globally up-dated during the training process for users u ∈ U train . The learnedmeta-learner is further used to initialize the recommender modelfor new users u ∈ U test .

2.2 Recommender ModelSimilar to many previous works, we assume that the user prefer-ence is coming from a complex combination of his/her personalinformation such as user profiles, user rating records, and the itemprofiles.

2.2.1 Embedding: pu → eu , pi → ei . We use user profile pu torepresent the initial user preference for the following considerations.First, user profile normally includes general information such asage groups and locations. In a cold-start scenario, where thereare only limited user-item interaction records, this will providepotential user preference for the recommenders. Second, traditionalone-hot user representation (by a unique id) is strongly relied oncollaborative filtering techniques. The fine-tuned model is hard toadapt to new users. Similarly, we use pi to denote the item profilefor learning the item embedding.

To learn the user and item embedding vectors eu ∈ Rde and ei ∈Rdu from pu ∈ Rdu and pi ∈ Rdi , the simplest way is constructinga multi-layer fully connected neural network, i.e.

eu = fθu (pu ), ei = fθi (pi ) (1)

where de is the embedding size; f denotes the fully connectedlayers; du and di stand for the dimension of the user profile vectorand item profile vector; θu and θi are the parameters of the fullyconnected layers for learning user and item embedding, respectively.We will omit similar notations in the rest of the paper.

2.2.2 Recommendation: (eu , ei ) → yu,i . Given the user embeddingeu , and a list of rated item embeddings ei for i ∈ IQu , we get theprediction of preference score yu,i for each item by:

ˆyu,i = fθr (eu , ei ) = FCθr (Mu, I · [eu , ei ]) (2)

where [eu , ei ] is the concatenation of the user embedding andthe item embedding, and FC denotes the fully connected layers.Mu, I ∈ Rde×2de is a matrix that includes the fast weights ofthe recommender model for user u, which is extracted from thetask-specific memory MU , I according to the user profile pu , i.e.Mu, I ← (pu ,MU , I ). The task-specific memoryMu, I for useru, willbe locally updated (i.e. during the learning on support set of user u)for personalized recommendation. We will introduce more detailsabout the task-specific memory in the further parts.

2.3 Memory-Augmented Meta-Optimization2.3.1 Feature-specific Memory: (pu ,MU ,MP ) → bu . Recall thatthe parameters used for extracting user and item embedding are θuand θi , traditional meta optimization approach will learn the globalparameters ϕu and ϕi for initialization, i.e. θu ← ϕu , θi ← ϕi .Here for addressing the single initialization problem, we introducefeature-specific memories, i.e. the user embedding memoryMU andthe profile memoryMP , to help the model initialize a personalizedparameter θu . The profile memoryMP stores information relevantto user profiles pu to provide the retrieval attention values au . Theretrieval attention values are applied for extracting informationfrom user embedding memoryMU , where each row ofMU keepsthe according fast gradients (or bias terms). Together, the two mem-ory matrices will help to generate a personalized bias term bu wheninitializing θu , i.e. θu ← ϕu − τbu . Here the bias term bu can beregarded as a personalized initialization parameter for guiding theglobal parameter ϕu to fast adapt to the case of user u; the τ is ahyper-parameter for controlling how much bias term is consideredwhen initializing θu .

In details, given a user profile pu , the profile memory MP ∈RK×du will calculate the attention values au ∈ RK by

au = attention(pu ,MP ) (3)

where attention function calculates the cosine similarity betweenthe user profile and the user profilememory, and then be normalizedby softmax function. The dimension K denotes the number of userpreference types, which is a predefined number before the trainingprocess. We obtain the personalized bias term bu by

bu = a⊤uMU (4)

where MU ∈ RK×{dθu } stores the memory of the fast gradients.Notice that the user embedding model may comprise more thanone neural layer and more than one parameter, which meansMUis not a numerical matrix but stores all the fast gradients with thesame shape as the parameters in the user embedding layers, so here

dθu denotes the dimension of the parameters in user embeddinglayers.

Before the training process, the two memory matrices are ran-domly initialized, and will be updated during the training process.Specifically, profile memory will be updated by:

MP = α · (aup⊤u ) + (1 − α)MP (5)

where (aup⊤u ) is the cross product of au and pu , α is a hyper-parameter to control how much new profile information is added.Here we add an attention mask au when add the new informationso that the new profile information will be attentively added tothe memory matrix. Similarly, the parameter memory MU will beupdated by

MU = β · (au∇θu (L( ˆyu,i ,yu,i ))) + (1 − β)MU (6)

where L( ˆyu,i ,yu,i ) denotes the training loss, and β is the hyper-parameter to control how much new information is kept.

2.3.2 Task-specific Memory: (au ,MU , I ) → Mu, I . The user prefer-ence matrixMu, I ∈ Rde×2dd serves as fast weights or a transformmatrix for the recommender model from the user and item em-bedding (see equation (2)) that is extracted from the memory cubeMU , I ∈ RK×de×2de , where K is the same notation for the dimen-sion of feature-specific memory that denotes the number of userpreference type. Similar to the feature-specific memory, which fol-lows the idea of Neural Turing Machine (NTM)[13], the memorycube MU , I have a read head to retrieve the memory and a writehead to update the memory. Similarly, we attentively retrieve thepreference matrixMu, I fromMU , I by:

Mu, I = a⊤u ·MU , I (7)

where au ∈ RK is learned from equation 3. The write head willwrite the updated personal preference memory matrixMu, I to theMU , I after the learning on the support set.

MU , I = γ · (au ⊗ Mu, I ) + (1 − γ )MU , I (8)

where ⊗ denotes the tensor product, γ is a hyper-parameter tocontrol how much new preference information is added.

2.3.3 Local Update. Traditionally, the parameters of a neural net-work are initialized by randomly sampling from a statistical dis-tribution. Given sufficient training data, the randomly initializedparameters can usually converge to a good local optimum but maytake a long time [8]. In the cold-start scenario, random initializationcombined with limited training data can lead to serious over-fitting,which makes the trained recommender insufficient to generalizewell. Inspired by recent works of meta-training[15], we initializethe recommender parameters from the global initial values.

At the beginning of the training process, we randomly initializethe global parameters, i.e. ϕu , ϕi , ϕr ,MU ,MP ,MU , I . For each useru ∈ U train , we have support set and query set. During the locallearning phase (i.e. learning on the support set), we initialize thelocal recommender parameters by:

θu ← ϕu − τbu (9)θi ← ϕi ,θr ← ϕr (10)

where bu is obtained via equation (3-4). Then we obtain the task-specific memory matrix Mu, I by equation (7). The prediction of

Algorithm 1: Training process of MAMOInput: Training user setU train ; User profile

{pu |u ∈ U train }; Item profile {pi |i ∈ (ISu , IQu )}; User

ratings {yu,i |u ∈ U train , i ∈ (ISu , IQu )};

Hyper-parameters α , β , γ , τ , ρ, λOutput:Meta parameters ϕu , ϕi , ϕr ,MP ,MU ,MU , I

1 Randomly initialize the meta parameters ϕu , ϕi , ϕr ;2 Randomly initialize the memoriesMP ,MU ,MU , I ;3 while Not Done do4 for u ∈ U train do5 Calculate bias term bu ← (pu ,MU ,MP ) by Eq. (3-4);6 Initialize the local parameters θi , θu , θr by Eq. (9-10);7 Initialize the preference memoryMu, I ← (au ,MU , I )

by Eq. (7);8 for i ∈ ISu do9 Get user and item embedding eu and ei by Eq. (1);

10 Get prediction of ˆyu,i by Eq. (2);11 Local updateMu, I ;12 Local update θu , θi , θr by:

θ∗ ← θ∗ − ρ · ∇θ∗L(yu,i , ˆyu,i );13 end14 end15 Update feature-specific memoryMP ,MU by Eq. (5-6);16 Update task-specific memoryMU , I by Eq. (8);17 Update global parameters ϕu , ϕi , ϕr by:

ϕ∗ ← ϕ∗ − λΣu ∈U trainΣi ∈IQu∇L(Rθ̂∗ );

18 end

ratings for items i ∈ ISu is based on equation (2). The optimizationgoal in local training is to minimize the loss of the recommendationfor a single user, i.e. updating the local parameters by minimizingthe prediction loss L(yu,i , ˆyu,i ). Thus, the local parameters will beupdated by:

θ∗ ← θ∗ − ρ · ∇θ∗L(yu,i , ˆyu,i ) (11)where ∗ could be either i , u, or r ; ρ is the learning rate for updatingthe local parameters. The preference matrixMu, I will also be locallyupdated via back-propagation.

2.3.4 Global Update. The aim of the meta optimization is to mini-mize the expected loss on the local query set i ∈ IQu foru ∈ U train .Here, the parameters of the meta-learner include: shared initial pa-rameters ϕu , ϕi and ϕr ; feature-specific memories, i.e. profile mem-ory MP and user embedding memory MU ; and the task-specificmemoryMU , I . The gradients related to the meta-testing loss, whichwe call meta-gradient, can be computed via back-propagation. Themeta-gradient may involve higher-order derivatives, which areexpensive to compute when the depth of the neural nets is deep.Therefore, MAML[22] takes one-step gradient descent for meta-optimization. We take similar ideas, where after the local trainingon the support set, we update the global parameters according tothe loss on query sets.

Suppose the recommender model is denoted as Rθ combinedwith a task-specific memoryMu, I for useru, where θ = {θu ,θi ,θr }.

After the local training on support set, we get the model Rθ̂ withupdated parameters θ̂ . Our goal is minimizing the training lossfor users u ∈ U train on query sets for i ∈ IQu . Then, the globalparameters are updated by

ϕ∗ ← ϕ∗ − λΣu ∈U trainΣi ∈IQu∇L(Rθ̂∗ ) (12)

Meanwhile, the feature-specific memoriesMP andMU will be up-dated by equation (5) and (6); the task-specific memoryMU , I willbe updated by equation (8). The pseudo code of the training processis listed in algorithm 1.

3 EXPERIMENTS3.1 Datasets3.1.1 Datasets. We use two widely used public available datasetsfor evaluation: MovieLens 1M2 and Book-crossing3, which haveboth user information and item information. MovieLens 1M in-cludes around 1 million ratings from about 6 thousand users forover 3 thousand movies, and the ratings range from 1 to 5. For theBook-crossing dataset, we filter the records that users or items donot have relevant profiles. The processed dataset includes about600 thousand ratings from around 50 thousand users for over 50thousand books, the ratings are between 1 and 10. See appendixA.1 for more details.

3.1.2 Data preprocessing. We use different strategies when learn-ing the feature representation. For features have single categoricalvalue, such as location and occupation, each feature is denoted byindex and is represented with a randomly initialized embeddingvector; we use similar approaches to process the numerical featuressuch as the publication year and age group. For features that mayhave multiple categories, such as movie genres and directors, weuse one-hot representation and then transform them into vectorsthat have same dimension with other feature vectors.

3.1.3 Training and testing dataset. Each user is regarded as a sam-ple in the dataset. We randomly separate the users into trainingand testing users with ratio 80:20. The history records for a singleuser are further divided into support set and query set. We trim thenumber of rating records for each user as with 20 records to forcethe model to learn from few samples. In default settings, we con-sider the first 15 items for a user as the support set and the othersas the query set. A detail is that we sort these items according tothe user review time. By doing so, the rated items in query set arelogically regarded as ’new items’ for a user. We will further discusswhether the ratio of training dataset or the number of cases in thesupport set will affect the model performance.

3.1.4 Cold-start scenarios. We further consider the recommenda-tion performance on four scenarios: 1) existing users for existingitems (W-W) ; 2) existing users for cold items (W-C); 3) cold usersfor existing items (C-W); and 4) cold users for cold items (C-C).For the MovieLens dataset, we classify the users into warm or coldusers according to their first comment time. The first comment timein the MovieLens dataset ranges from 2000-04-26 to 2003-03-21. Wefound most users (about 90%) provide their first comments before

2https://grouplens.org/datasets/movielens/3http://www2.informatik.uni-freiburg.de/~cziegler/BX/

2000-12-03. By dividing the users based on this time, we have 5,400warm users and 640 cold users. As for the items, we regard itemswith less than 10 ratings as cold items, where we get 1,683 warmitems and 1,645 cold items. For the Book-crossing dataset, wherethe rating time is not provided, we assume the order of the userids is consistent with the order of the user registration time. Thus,we assume the first 90 percent of the users are warm users and theothers are cold users. Similarly, we regard items with more than 5ratings as warm items, from which we get 628 warm items and theothers as cold items.

3.2 Parameter StudiesHere we show the parameter studies on several key parametersof our method: the model set-up parameters when initializing thetraining and testing dataset; the model structure parameters forconstructing the recommender models; and the hyper-parametersduring the learning process. We present the results under twoevaluation metrics, i.e. Mean Absolute Error (MAE) and normalizeddiscounted cumulative gain (NDCG):

MAE =1

|U test | Σu ∈U test1

|IQu |Σi ∈IQu

|yu,i − ˆyu,i | (13)

NDCG@N =1

|U test | Σu ∈U testDCG@N

IDCG@N(14)

DCG@N = ΣNn=12yu,n − 1log(n + 1) (15)

where N is the number of instances in the query set for each user;DCG@N calculates the top − N actual rating values sorted by pre-dicted rating values; and IDCG@N calculates the top − N sortedactual rating values, i.e. the most possible values, for DCG@N .MAE evaluates the accuracy of rating prediction, where a lowervalue indicates better model performance. NDCG@N considers thepreference ordering performance on observed query sets, where ahigher value indicates a better performance. The experiments areconducted on MovieLens dataset.

3.2.1 Model set-up parameters. Here we consider the model per-formance under different separating ratios for training-testing orsupport-query sets. The experimental results (Figure 2 (a)) suggesta higher ratio of the training set improves the model performance;while the performance for training with only half of the users is stillacceptable, which indicates the effectiveness of the meta-trainingapproach. As for the sample size of the support set, where we con-trol the maximum of rating records for a user as 20, we comparethe results with support sample size between 5 to 15, where we usethe last 5 samples for each user as the query sample set for a faircomparison. According to Figure 2 (b), we can find that a largersample size provides better results, while the model can also pro-vide acceptable predictions with smaller sample size, which showsits capacity in cold scenarios.

3.2.2 Model structure parameters. The settings of the parametersfor deep neural nets, especially the number of layers and the dimen-sion of layer nodes, can sometimes affect the model performance.Generally, a network with large dimension and a complex structuremay provide accurate predictions but is data hungry and slow inconvergence. In our work, we use fully connected layers to learn

the user and item embeddings. According to Figure 2 (c)-(d), whichshow the model performance under different number of embeddinglayers and embedding size de , we could see that the number ofneural layers has slight impacts on the model performance, whiletoo shallow or too deep layers may lead to bad results. A moderatesetting of the embedding size can provide acceptable predictionresults and require less training time.

3.2.3 Hyper-parameters. We have hyper-parameters α and β (rang-ing from 0 to 1) for globally updating the profile memoryMP anduser embedding memory MU in feature-specific memory, and γfor globally updating the task-specific memoryMU , I . The hyper-parameters control how much new information is added to thememory matrices. Figure 2 (e)-(f) show the parameter sensitivityfor parameter α and β . For parameter α , values around 0.5 providebetter performance of the models, because of the update strategy ofthe memory matrices. Since the profile memory is randomly initial-ized and is not updated by back-propagation, the profile memoryrequires more new information to complete the distribution of theuser profiles. While for the user embedding memory, too much newinformation may cause chaos in existing memory, where β = 0.1provides the best performance. The parameter γ for task-specificmemory (not listed in the figures) has similar patterns with β , whereit provides best results with values around 0.1. We have ρ and λfor updating local or global parameters, and τ for providing per-sonalized bias term. Figure 2 (g)-(h) show the results for ρ and λ,where small learning rates provide best results, since a large valuemay make the model difficult in convergence. As for the parameterτ , which is not listed in the figures, we find the values around 0.1perform best.

3.3 Comparison Results3.3.1 Comparison Methods. We adopt the following representa-tive state-of-the-arts that apply the meta-learning idea into therecommender systems, where the first three methods are based onmeta-optimization, and the last method, which includes item-levelmodel and feature-level model, is based on memory networks.• MeLU [15]: get rating predictions by feeding the concate-nation of user and item embeddings into fully connectedlayers. The local parameter of the fully connected layers willbe locally updated for personalized recommendation. Theglobal parameter of the recommender and the parameters ofembedding layers will be globally updated for all the users.• MetaCS-DNN [3]: follows a similar idea of MeLU whenconstructing the recommender model, i.e. several fully con-nected layers, the difference is the local and global parame-ters involve all parameters from the inputs to the predictions.• s2 Meta [8]: uses a deep neural net as the recommendermodel and updated via meta-optimization approach. Specifi-cally, it introduced update and stop controllers to update thelocal parameters.• RUM: [6] uses neural matrix factorization as the recom-mender model, where the score for an item is the productof the user and item embeddings. The user embedding islearned from a user’s intrinsic embedding and a memoryembedding. The memory embedding is learned by eitheritem-level or feature-level memories, i.e. item-level RUM

(a) (b) (c) (d)

(e) (f) (g) (h)

Figure 2: Parameter sensitivity in different settings.

Table 1: Comparison Results

Method Metrics MovieLens-1M Book-crossingW-W W-C C-W C-C W-W W-C C-W C-C

MeLU MAE 0.7661 0.9361 0.7884 0.9299 0.7799 2.1047 1.8701 2.1475NDCG@3 0.8904 0.7990 0.8810 0.8011 0.9572 0.8441 0.8527 0.8410

MetaCS-DNN MAE 0.9047 1.1694 1.0625 1.2012 1.6206 2.1457 2.2648 2.3088NDCG@3 0.9090 0.7715 0.8559 0.7680 0.8860 0.8365 0.8202 0.8160

s2 Meta MAE 0.7567 0.8860 0.8443 0.9130 1.5147 1.9767 1.8738 2.0921NDCG@3 0.8870 0.8323 0.8401 0.8148 0.8781 0.8463 0.8490 0.8422

Item-level RUM MAE 0.8874 1.3424 1.2655 1.3509 1.4611 2.2857 2.2608 2.3197NDCG@3 0.9102 0.7692 0.7420 0.7680 0.8920 0.8265 0.8202 0.8160

Feature-level RUM MAE 0.8739 1.2439 1.2488 1.2773 1.3945 2.0837 2.0322 2.1260NDCG@3 0.9120 0.7721 0.7642 0.7547 0.8909 0.8430 0.8338 0.8273

MAMO MAE 0.8725 0.9306 0.8967 0.8894 1.4879 1.7379 1.6217 1.8188NDCG@3 0.8866 0.8315 0.8799 0.8709 0.8879 0.8402 0.8565 0.8384

and feature-level RUM. The item-level RUM stores andextracts the memory according to different items, while thefeature-level RUM considers the similarity of the differentfeatures. Here, the memory matrix is initialized by eachuser’s history records and is locally updated for personalizedrecommendation.

The parameter settings for our method and the comparisonmethodscan be found in appendix A.2.

3.3.2 Comparison Results. The comparison results are listed inTable 1. Generally, we can see that the meta-optimization basedmethods show outstanding performance in cold scenarios, whileRUM outperforms other methods in warm situations. This can beattributed to the stronger capability of meta-optimization approachin capturing the general preferences. Since the memory matrices de-signed in RUM store only the personal history information, it needsmore history records to establish an efficient memory matrix. Com-paring MetaCS-DNN and MeLU, which utilize different strategiesfor updating embedding parameters, the results show that locallyupdating the embedding parameters performs better than globallyupdating the embedding parameters. We can see that our method

shows stable and well performance in different scenarios, whichshows the effectiveness of the meta-augmented meta-optimizationstrategy: learning a personalized initialization of local parametersfrom the memories.

3.4 DiscussionMAMO has two groups of memories. The first group includes userprofile memoryMP and user embedding memoryMU that are uti-lized for providing personalized bias term when initializing thelocal parameters. The second group includes the task-specific mem-oryMU , I . In this section, we will discuss the impact of these twogroups of memories. Also, we predefined K user types when con-structing the aforementioned memories. We will discuss how to setan appropriate K and present an example of the standard users forK user preference patterns.

3.4.1 Impact of Personalized Bias Term. The basic idea of meta-optimization process is learning a sharing global parameter ϕ wheninitializing the personalized local parameter θ (see Figure 3 (a)). Foraddressing the potential local optima issues by the unique globalsharing parameter for most current meta-optimization based works,

φL1

L2 L3

θ1

θ2 θ3

(a)

L1

L2 L3

φ

b1

b2 b3

θ1

θ2 θ3

(b)

Figure 3: The major difference between MAML and ourmethod. Red lines stand for the global/meta-optimization,the blue lines stand for the local learning/adaption.

(a)Training: |S|=10 (b)Testing: |S|=10

(c)Training: |S|=5 (d)Testing: |S|=5

Figure 4: The performance during training process and test-ing process with different settings of support sample size ondifferent recommender models.

we introduce two memory matrices to provide a personalized biasterm bu when initializing the local parameters θu when learningthe user embedding. Specifically, the profile memory MP storesK types of user profiles, andMU stores corresponding bias terms.Then, the local parameters will be locally updated for personal-ized recommendation (see Figure 3 (b)). The comparison methods,MeLU and MetaCS-DNN, both utilize MAML for meta-optimization.According to the comparison results, we can see that our strategyoutperforms these two methods in cold scenarios, especially forcold users. The reason may lie in that our optimization approachtakes the user profile into consideration. The profile memory willautomatically cluster users with similar profiles to provide fast biasterms.

3.4.2 Impact of Preference Memory. We also introduce the task-specific memoryMU , I that contains K types of preference matricesduring the recommendation process. To see whether it helps therecommendation process, we compare it with different designs ofrecommender models. The first is predicting the ratings by theconcatenation of the user and item embedding through severalfully connected layers, denoted by DNN. The second is taking the

(a) (b)

Figure 5: (a)Performance with different K . (b) Example forrepresentative users when K = 2.

idea of neural matrix factorization [14], which multiplies the userembedding and item embedding as the predictions, denoted byNMF. The results are shown in Figure 4, where (a), (c) show theperformance on the query dataset during the training process; (b),(d) show the performance on the query dataset during the testingprocess. We can observe that DNN and NMF converge fast in thetraining process but perform unwell on testing dataset with smallsupport sample size, while our method needs more steps to storethe preference information but can learn fast during the testingprocess.

3.4.3 Discussion of Preference Type. In this work we predefinedK user types when constructing the proposed memories, whichcan be regarded as the number of clusters of users based on theuser profiles. Figure 5 (a) shows the model performance underdifferentK . We can see that theK values around 2-4 achieve the bestperformance. A larger K has potential in providing more accurateguidance in recommendation, but it will take more computationcost (each type inMU stores parameters with the same shape as allthe network parameters in user embedding networks). In Figure 5(b), we present the case whenK = 2. We selected two representativeuser profiles which are most similar to MP , the distributions arefrom the top 100 users that belong to these two types.

3.4.4 Limitations and Future work. In cold-start scenarios, auxiliaryinformation is valuable for providing potential recommendations.Our work targets at the situations that users or items have limitedinteraction histories and utilizes the idea of few-shot learning toprovide recommendations. We assume we have enough essentialprofile details of the users or items. During the data preprocess-ing process, we filter the data that are without relevant profiles.However, in the real-world cases, the auxiliary information is notalways attainable, where our model becomes inefficient under suchcircumstance. In future works, we plan to leverage the knowledgefrom multi-modal studies [2] to address this issue. For example, Wuet al. [29] design a multimodal variational autoencoder that learnsa joint feature distribution under any missing modalities.

4 RELATEDWORK4.1 Cold-start Problem in Recommender

SystemsIt is still a tricky and significant problem for recommenders toaccurately recommend items to users. Some solutions in solving thisproblem have been provided in current publications [20], involving

second-domain knowledge transfer [16], auxiliary and contextualinformation [21, 31], active learning [35] and deep learning [9].

Commonly, it is reported that the more information the bet-ter recommendation results are. [19] adds the matrix factorizationwith clusters to recommendations of cross-domains. Similarly, [16]presents an innovative model of cross-domain recommendationaccording to the partial least squares regression (PLSR) analysis.Both PLSR-CrossRec and PLSR-Latent can be utilized in ratingof source-domain for better predicting ratings of cold-start users.Apart from leveraging auxiliary information from another domain,some researchers have regarded representative item content asauxiliary information to learn representative latent factor whencoped with the cold-start problem. According to implied feedback,[21] presents an approach named visual-CLiMF to learn represen-tative latent factors for cold start videos, where emotional aspectsof items are incorporated into the latent factor representations ofvideo contents. In order to better use content characteristics in fur-ther latent characteristics, [7] proposed a next-song recommendersystem for cold-start recommendation by mapping both learningand updating within spaces of the audio characteristic and the itemlatent. In addition, active learning has found its way in tacklingboth the user cold-start problem in both users [10] and the items[1]. [35] combines the active learning approach with itemâĂŹsattribute information to deal with the cold-start problem in items.More recent works take advantage of deep learning [9, 27, 32]. [18]proposes a multiplex interaction-oriented service recommendationapproach (MISR), which merged different interactions into a deepneural network to search latent information so that new users canbe better dealt with. [27] proposes a hybrid recommendation modelin researching the content characteristics of items by means ofa deep learning neural network and then exploited them to thetimeSVD++ collaborative filtering model.

4.2 Meta-learning for Recommender SystemsMeta-learning, namely learning to learn, is learning across varioustasks with fewer training samples in each task, which can be easilyadapted to new tasks [24]. In recent years, meta-learning has beenattracting much attention to alleviate cold-start problems [5, 15, 34],and most of them adopted optimization-based meta-learning ap-proach and chose model-agnostic meta-learning (MAML) [11] formodel training. Generally, those works define a recommendationmodel Rθ with parameter θ , and a meta-learnerM(ϕ). Modelingeach user’s preference is regarded as a learning task, and the usersare divided into training and testing users. The initialization ofparameter θ is defined by some function θ ←M(ϕ), e.g. in a sim-plest case, θ ← ϕ. During the training process, the parameter ofthe recommendation model, i.e. θ , will be locally updated by mini-mizing the recommendation loss L(Rθ (Dsuppor t )) on the supportset Dsuppor t (the history ratings by a user) for a single user; andthen used to retrieve the recommendation loss L(Rθ (Dquery )) onthe query set Dquery . The parameter of the meta-learner will beglobally updated by minimizing the sum of recommendation lossΣu ∈U train (L(Rθ←ϕ (Dquery ))) for all users in the training dataset.Then, the meta-learner will guide the learning process for newusers by providing the initialization of parameter θ , which can

expedite the learning process of the recommendation models fortesting users.

The major differences among the above works lie in the design ofthe recommender model Rθ and the meta-optimization approachM(ϕ). For example, [15] targets at a rating prediction problemwhere they feed the concatenation of user and item embedding intofully-connected layers to get predictions. They locally update theparameters of neural layers to get personalized recommendationand globally update the parameters of embedding learning and aglobal parameter of neural layers. [8] constructs a deep neural netsas the recommender model, and they design an input gate and aforget gate during updating the local parameters. One limitation ofthe current meta-optimization approach for recommendation is thatmost works learn a shared global initialization parameter, whichmeans the initialization parameter is same for all users. This maylead the recommender model to the local optima problem and tobe slow in convergence. To address this issue, our work introducestwo memory matrices to provide personalized bias terms wheninitializing the parameters.

4.3 Memory-augmented Neural NetworksWith the ability to express, store, and manipulate the records explic-itly, dynamically, and effectively, external memory networks [23]have gained popularity in recent years in fields such as question-answering systems [30] and knowledge tracking [12]. One branchof the memory neural networks is based on Neural Turing Machine(NTM) [13]: the memory is normally stored in a matrix with aread head to extract the information from the memory and a writehead to update the memory at each time step. Such features makethe NTM a good module for meta-learning or few-shot learning.Following this idea, [22] proposes Memory-augmented Neural Net-works (MANN). Similar to NTM, they design a read controller tolearn a key vector vt from the inputs at time t , and vt is used tolearn the rating weightswr

t for the rows in the memory matrixMt ;the retrieved vector is the sum of rows in memory matrix with theabove attention values, i.e. Σkwr

t (k)Mt (k). Then, for updating thememory, the authors propose usage weightswu

t to evaluate the us-age of the rows in the memory matrix. The writing weightsww

t arelearned from the previous reading weights and the usage weights.Last, the memory is updated byMt (k) ← Mt−1(k) +ww

t (k)vt .The work by [6] is one of the first works that integrate MANN

into recommendation tasks. They consider the matrix factoriza-tion model as a neural network, where the score yu,i for an itemi from user u is predicted from the user and item embeddings, i.e.yu,i = e⊤u ei . They propose memory enhanced the user embed-ding, where the user embedding is learned from a user’s intrinsicembedding e∗u and a memory embedding eMu = read(Mu , ei ), i.e.eu ← f (e∗u , eMu ). The memory embedding eMu reads from the userpersonalized memory matrixMu to retrieve the related informationfor item i according to the item embedding ei . Another work by[17] adds a gate mechanism to control how much past memoryand current memory are kept. Different from these works wherethe memory matrices are designed for each user and cannot shareamong different users, we propose two global sharing memories:feature-specific memory and task-specific memory. The feature-specific memory includes user profile memory and user embedding

memory. Given a user, this memory will extract the parameter mem-ory according to the similarity between the user profile and the userprofile memory. The task-specific memory stores the preferenceinformation, which serves as fast weights for the recommendermodel, to alleviate the need for storing copies of neural activitypatterns.

5 CONCLUSIONA common challenge for most current recommender systems is thecold-start problem. Recently, inspired by the progress of few-shotlearning, some works leverage the meta-optimization idea into therecommendation. The core idea is learning a global sharing initial-ization parameter of the recommender model for all users and thenupdating the local parameters to learn personalized recommendermodel for single users. A common limitation for most current worksis that the global sharing initialization parameter is unique for allusers, which may lead the recommendation model into local op-tima for users with distinct preference patterns. For addressing thisissue, in this work, we design two memory matrices to provide per-sonalized initialization for recommender models: feature-specificmemory that provides a personalized bias termwhen initializing therecommender model, and a task-specific memory to guide the rec-ommendation process. We evaluate the proposed methods on twopublic available datasets and provide details of the implementation.The experimental results show the effectiveness of our method.

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A APPENDIXA.1 Dataset DetailsA.1.1 Movielens. The user profile includes gender (male or female),age group (under 18, 18-25, 26-35, 36-45, 46-50, 51-56, 56+), and21 different occupations (e.g. student, engineer). The item profileincludes movie’s release year, genres (e.g. action or adventure),director (one or more directors), and rate (e.g. R, PG). The meanrating value is 3.58, and the rating comment time is between 2000-04-26 and 2003-03-01. In the raw data, each user has minimum 20rating histories. We sort the items rated by a user according to theirreview time, and we trim the dataset, i.e. each user having 20 ratingrecords, to force the model to learn from few shot cases.

A.1.2 Book-crossing. The raw Book-crossing data contains manymissing and misleading values. The user information includes userage and location. The original user age ranges from 0 to 237, whichis in contrast of real cases. Thus, we control the age interval as5 to 110. The location includes city, state, and country. We onlykeep the country information for both missing value and privacyconsideration. The filtered data has users from 65 different countries.The item information includes the publication year (ranges from1500 to 2010), author (25593 unique authors), and publisher (5254unique publishers). The Book-crossing dataset does not containtime information for the ratings, thus we assume the data storedin the public dataset are based on the review time, where we keepthe order of items that rated by a user to make our dataset. We alsokeep 20 rating records for each user for few-shot learning.

A.2 Compared methodsA.2.1 Code. The code of MeLU4 and S2 Meta5 are provided by theauthors. We modify the input and evaluation modules to fit ourexperimental settings. For MetaCS-DNN, which has similar idea ofMeLU, we modify the code of MeLU to implement it. As for RUM,the code is not published; thus, we implement them with Pytorch.

A.2.2 Parameter configuration. For MeLU, we use the default pa-rameter settings in the published code. For S2 Meta, we implementthe code with the parameter settings for Movielens Dataset. Forother two comparison methods, we use the suggested parameterswhen reproduce them. ForMetaCS-DNN, the global update learningrate is set to 0.4. For RUM, the learning rate of SGD is determinedby grid search in the range of [1, 0.1, 0.01, 0.001, 0.0001], and thenumber of memory slot K is empirically set as 20. The MERGEparameter α is searched in the range of [0,1] with step 0.1. The em-bedding dimension and regularization parameters are determinedby grid search in the range of [10, 20, 30, 40, 50] and [0.1, 0.01, 0.001,0.0001], respectively.

A.2.3 The evaluation metrics in cold-scenarios. We provided ourdefinitions for cold-users and cold-items in section 3.1.4 and evalu-ated the performance under the evaluation metricsMAE (see Eq. 13)and NDCG@N (see Eq. 14). Notice that the users could be eitherwarm users or cold users, and the items rated by a user could beeither warm items or cold items – we label each rating record asin four cold-start scenarios. For example, for a cold user, the rated

4https://github.com/hoyeoplee/MeLU5https://github.com/THUDM/ScenarioMeta

items are labeled as either warm items (C-W) or cold items (C-C).The calculation forMAE in four cold-start scenarios is easy, wherewe can simply calculate the mean value for the ratings in the fourscenarios (i.e. W-W, W-C, C-W, and C-C). While for NDCG@N , thequery set for a user may contain less than N records in differentscenarios. Thus, for each scenario, we concatenate the results; sep-arate the results into small clips; calculate NDCG@N for each clip;and then take the mean value of the clips as the results.

A.3 Parameter settings.Our code is implemented with PyTorch 6 1.4.0 in Python 3.7 andruns on a Linux server with NVIDIA TITAN X. The processeddatasets will take about 2GB hard disk space. The default activationfunction is LeakyRelu 7. For Movielens dataset: the dimension ofthe embedding is set to 100; the default setting of the number oflayers is 2; the local learning rate ρ is 0.01 and the global learningrate λ is 0.05; the hyper-parameters α , β , γ and τ are set to 0.5, 0.05,0.1, and 0.1, respectively. For Bookcrossing dataset: the dimensionof the embedding is set to 50; the default setting of the number oflayers is 2; the local learning rate ρ is 0.01 and the global learningrate λ is 0.01; the hyper-parameters α , β , γ and τ are set to 0.5, 0.1,0.1, and 0.15, respectively. The random seed may affect the results– sometimes the results may show better or worse performancethan our presented results. The running time for one epoch overall users is about half an hour; so, a strategy is updating the globalparameters after learning from a batch of training users. Duringthe test process, the model updates as in algorithm 2.

Algorithm 2: Testing process of MAMOInput: Testing user setU test ; User profile {pu |u ∈ U test };

Item profile {pi |i ∈ (ISu , IQu )}; User ratings

{yu,i |u ∈ U test , i ∈ (ISu , IQu )}; Hyper-parameters α , β ,

γ , τ , ρ, λ; Meta parameters ϕu , ϕi , ϕr ,MP ,MU ,MU , I

Output: Predicted user preference {yu,i |u ∈ U test , i ∈ IQu }1 for u ∈ U test do2 Calculate bias term bu ← (pu ,MU ,MP ) by Eq. (3-4);3 Initialize the local parameters θi , θu , θr by Eq. (9-10);4 Initialize the preference memoryMu, I ← (pu ,MU , I ) by

Eq. (7);5 for i ∈ ISu do6 Get user and item embedding eu and ei by Eq. (1);7 Get prediction of ˆyu,i by Eq. (2);8 Local updateMu, I ;9 Local update θu , θi , θr by:

θ∗ ← θ∗ − ρ · ∇θ∗L(yu,i , ˆyu,i );10 end11 for i ∈ IQu do12 Get user and item embedding eu and ei by Eq. (1);13 Get prediction of ˆyu,i by Eq. (2);14 end15 end

6https://pytorch.org/7https://en.wikipedia.org/wiki/Rectifier_(neural_networks)