ColdNAS: Search to Modulate for User Cold-Start Recommendation

Making personalized recommendation for cold-start users is particular challenging, as these users only have a few interaction histories (Schein et al., 2002). In the past, collaborative filtering (CF)-based (Koren, 2008; Sedhain et al., 2015; He et al., 2017) methods, which make predictions by capturing interactions among users and items to represent them in low-dimensional space, obtain leading performance in RSs. However, these CF-based methods make inferences only based on the user’s history. They cannot handle user cold-start problem. To alleviate the user cold-start problem, content-based methods leverage user/item features  (Schein et al., 2002) or even user social relations (Lin et al., 2013) to help to predict for cold-start users. The recent deep model DropoutNet (Volkovs et al., 2017) trains a neural network with dropout mechanism applied on input samples and infers the missing data. However, it is hard to generalize these content-based methods to new users, which usually requires model retraining.

A recent trend is to model user cold-start problem as a few-shot learning problem (Wang et al., 2020). The resultant models learn the ability to quickly generalize to recommend for new users with a few interaction histories. Most works mainly follow the classic gradient-based meta-learning strategy MAML (Finn et al., 2017), which first learns a good initialized parameter from training tasks, then locally update the parameter on the provided interaction history by gradient descent. In particular, existing works consider different directions to improve the performance: MeLU (Lee et al., 2019) selectively adapts model parameters to the new task in the local update stage, MAMO (Dong et al., 2020) introduces external memory to guide the model to adapt, MetaHIN (Lu et al., 2020) uses heterogeneous information networks to leverage the rich semantics between users and items, REG-PAML (Yu et al., 2021) proposes to use user-specific learning rate during local update, and PAML (Wang et al., 2021) leverages social relations to share information among similar users. While these approaches can adapt models to training data, they are computationally inefficient at test-time, and usually require expertise to tune the optimization procedure to avoid over-fitting.

Neural architecture search (NAS) targets at finding an architecture with good performance without human tuning (Hutter et al., 2019). Recently, NAS methods have been applied in RSs. SIF (Yao et al., 2020a) searches for interaction function in collaborative filtering, AutoCF (Gao et al., 2021b) further searches for basic components including input encoding, embedding function, interaction function, and prediction function in collaborative filtering. AutoFIS (Liu et al., 2020), AutoCTR (Song et al., 2020) and FIVES (Xie et al., 2021) search for effective feature interaction in click-through rate prediction. AutoLoss (Zhao et al., 2021) searches for loss function in RSs. Due to different problem settings, search spaces needs to problem-specific and cannot be shared or transferred. Therefore, none of these works can be applied for user cold-start recommendation problem. To search efficiently on the search space, one can choose reinforcement learning methods (Baker et al., 2017), evolutionary algorithms (Real et al., 2019), and one-shot differentiable architecture search algorithms (Liu et al., 2019; Pham et al., 2018; Yao et al., 2020b). Among them, one-shot differentiable architecture search algorithms have demonstrated higher efficiency. Instead of training and evaluating different models like classical methods, they optimize only one supernet where the model parameters are shared across the search space and co-adapted.

Let user set be denoted $\mathcal{U}=\{u_{i}\}$, where each user $u_{i}$ is associated with user features. The feature space is shared across all users. Let item set be denoted $\mathcal{V}=\{v_{j}\}$ where each item $v_{j}$ is also associated with item features. When a user $u_{i}$ rates an item $v_{j}$, the rating is denoted $y_{i,j}$. In user cold-start recommendation problem, the focus is to make personalized recommendation for user $u_{i}$ who only has rated a few items.

Following recent works (Bharadhwaj, 2019; Lu et al., 2020; Lin et al., 2021), we model the user cold-start recommendation problem as a few-shot learning problem. The target is to learn a model from a set of training user cold-start tasks $\mathcal{T}^{\text{train}}$ and generalize to provide personalized recommendation for new tasks. Each task $T_{i}$ corresponds to a user $u_{i}$, with a support set $\mathcal{S}_{i}=\{(v_{j},y_{i,j})\}_{j=1}^{N}$ containing existing interaction histories and a query set $\mathcal{Q}_{i}=\{(v_{j},y_{i,j})\}_{j=1}^{M}$ containing interactions to predict. $N$ and $M$ are the number of interactions in $\mathcal{S}_{i}$. $\mathcal{Q}_{i}$ and $N$ are small.

Existing modulation-based user cold-start works can be summarized into the following modulation framework consisting of three parts, i.e., embedding layer, adaptation network and predictor, as plotted in Figure 1.

• •

  The embedding layer $E$ with parameter $\bm{\theta}_{E}$ embeds the categorical features from users and items into dense vectors, i.e., $(\bm{u}_{i},\bm{v}_{j})=E(u_{i},v_{j};\bm{\theta}_{E})$.

• •

  The adaptation network $A$ with parameter $\bm{\theta}_{A}$ takes the support set $\mathcal{S}_{i}$ for a specific user $u_{i}$ as input and generates user-specific adaptive parameters, i.e.,

  (1)

  $\displaystyle\bm{\Phi}_{i}=\{\bm{\phi}_{i}^{k}\}_{k=1}^{C}=A(\mathcal{S}_{i};\bm{\theta}_{A}),$

  where $C$ is the number of adaptive parameter groups for certain modulation structure.

• •

  The predictor $P$ with parameter $\bm{\theta}_{P}$ takes user-specific parameters $\bm{\phi}_{i}$ and $v_{q}\in\mathcal{Q}_{i}$ from the query set as input, and generate predictions by

  (2)

  $$\hat{y}_{i,j}=P((\bm{u}_{i},\bm{v}_{q}),\bm{\Phi}_{i};\bm{\theta}_{P}).$$

Comparing with classical RS models, the extra adaptation network is introduced to handle cold-start users. To make personalized recommendation, for each $u_{i}$, the support set $\mathcal{S}_{i}$ is first mapped to user-specific parameter $\bm{\phi}_{i}$ by (1). Then taking the features of target item $v_{q}\in\mathcal{Q}_{i}$, user features $u_{i}$, and the $\bm{\phi}_{i}$, prediction is made as (2). Subsequently, how to use the user-specific parameter $\bm{\phi}_{i}$ to change the prediction process in (2) can be crucial to the performance. Usually, a multi-layer perception (MLP) is used as $P$ (Cheng et al., 2016; He et al., 2017; Lin et al., 2021). Assume a $L$-layer MLP is used and $\bm{h}^{l}$ denotes its output from the $l$th layer, and let $\bm{h}^{0}=(\bm{u}_{i},\bm{v}_{q})$ for notation simplicity. For the $i$th user, $\bm{h}^{l+1}$ is modulated as

where $M^{l}$ is the modulation function, $\bm{W}^{l}$ and $\bm{b}^{l}$ are learnable weights at the $l$th layer. This $M^{l}$ controls how $\bm{h}^{l}$ is personalized w.r.t. the $i$th user. The recent TaNP (Lin et al., 2021) directly lets $M^{l}$ in (3) adopt the form of FiLM for all $L$ MLP layers:

FiLM applies a feature-wise affine transformation on the intermediate features, and has been proved to be highly effective in other domains (Requeima et al., 2019; Brockschmidt, 2020). However, users and items can have diverse interaction patterns. For example, both the inner product and summation have been used in RS to measure the preference of user over items (Koren, 2008; Hsieh et al., 2017).

In order to find the appropriate modulation function, we are motivated to search $M^{l}$ for different recommendation tasks. We design the following space for $M^{l}$:

where $\text{op}^{i}$’ are defined as

They are all commonly used simple dimension-preserving binary operations. We choose them to avoid the resultant $M^{l}$ being too complex, which can easily overfit for cold-start users.

The search space in (6) can be viewed as a binary tree, as shown in Figure 2(a). Since $M^{l}$ can be different for each layer, the size of this space is $6^{C\times L}$. A larger $C$ leads to a larger search space, which has higher potential of containing appropriate modulation function but is also more challenging to search effectively.

We aim to find an efficient and practicable search algorithm on the proposed search space. However, the search space can be very large, and differentiable NAS methods are known to be fragile on large spaces (Yu et al., 2019). In the sequel, we propose to first transform the original search space to an equivalent but much smaller space, as shown in Figure 2(a), where the equivalence is inspired by some similarities between the operations and the expressiveness of deep neural networks. On the transformed space, we design a supernet structure to conduct efficient and robust differentiable search.

Existing works in space transformation can be divided into three types. One is using greedy search strategy (Gao et al., 2021a). Methods of this kind explore different groups of architectures in the search space greedily. Thus, they fail to explore the full search space and can easily fall into bad local optimal. Another is mapping the search space into a low-dimensional one. For examples, using auto-encoder (Luo et al., 2018) or sparse coding (Yang et al., 2020). However, these types of methods do not consider special properties of the search problem, e.g., the graph structure of the supernet. Thus, the performance ranking of architectures may suffer from distortion in the low-dimensional space. ColdNAS belongs to the third type, which is to explore architecture equivalence in the search space. The basic idea is that if we can find a group of architectures that are equivalent with each other, then evaluation any one of them is enough for all architectures in the same group. This type of methods is problem-specific. For example, perturbation equivalence for matrices is explored in (Zhang et al., 2023), morphism of networks is considered in (Jin et al., 2019). The search space of ColdNAS is designed for modulation structures in cold-start problem, which has not been explored before. We theoretically prove the equivalence between the original space and the transformed space, which then significantly reduces the space size (Remark 2). Other methods for general space reduction cannot achieve that.

We use three benchmark datasets (Table 4): (i) MovieLens (Harper and Konstan, 2015): a dataset containing 1 million movie ratings of users collected from MovieLens, whose features include gender, age, occupation, Zip code, publication year, rate, genre, director and actor; (ii) BookCrossing (Ziegler et al., 2005): a collection of users’ ratings on books in BookCrossing community, whose features include age, location, publish year, author, and publisher; and (iii) Last.fm: a collection of user’s listening count of artists from Last.fm online system, whose features only consist of user and item IDs. Following Lin et al. (2021), we generate negative samples for the query sets in Last.fm.

We compare ColdNAS with the following representative user cold-start methods: (i) traditional deep cold-start model DropoutNet (Volkovs et al., 2017) and (ii) FSL based methods include MeLU (Lee et al., 2019), MetaCS (Bharadhwaj, 2019), MetaHIN (Lu et al., 2020), MAMO (Dong et al., 2020), and TaNP (Lin et al., 2021). We run the public codes provided by the respective authors. PNMTA (Pang et al., 2022), CMML (Feng et al., 2021), PAML (Wang et al., 2021) and REG-PAML (Yu et al., 2021) are not compared due to the lack of public codes. We choose a 4-layer predictor, more details of our model and parameter setting are provided in Appendix C.1. We also compare with a variant of ColdNAS called ColdNAS-Fixed, which uses the fixed FiLM function in (5) at every layer rather than our searched modulation function.

Table 2 shows the overall user-cold start recommendation performance for all methods. We can see that ColdNAS significantly outperforms the others on all the datasets and metrics. Among all compared baselines, DropoutNet performs the worst as it is not a few-shot learning method that the model has no ability to adapt to different users. Among meta-learning based methods, MeLU, MetaCS, MetaHIN and MAMO adopt gradient-based meta-learning strategy, which may suffer from overfitting during local-updates. In contrast, TaNP and ColdNAS learn to generate user-specific parameters to guide the adaptation. TaNP uses a fixed modulation structure which may not be optimal for different datasets, while ColdNAS automatically finds the optimal structure. Further, the consistent performance gain of ColdNAS over ColdNAS-Fixed validates the necessity of searching modulation structure to fit datasets instead of using a fixed one.

Table 3 shows the searched modulation structures. We find that the searched modulation structures are different across the datasets. No modulation should be taken at the last layer, as directly use user-specific preference possibly leads to overfitting. Note that all the operations in the transformed search space have been selected at least once, which means all of them are helpful.

Comparing time consumption to other cold-start models, ColdNAS only additionally optimizes a supernet with the same objective and comparable size. Table 5 shows the clock time taken by ColdNAS and TaNP which obtains the second-best in Table 2. As can be observed, the searching in ColdNAS is very efficient, as it is only slightly more expensive than retraining.

Finally, we conduct sensitivity analysis of ColdNAS on Last.fm.