The conventional approach to solving the recommendation problem greedily ranks
 individual document candidates by prediction scores. However, this method fails to
 optimize the slate as a whole, and hence, often struggles to capture biases caused
 by the page layout and document interdepedencies. The slate recommendation
 problem aims to directly find the optimally ordered subset of documents (i.e.
 slates) that best serve users’ interests. Solving this problem is hard due to the
 combinatorial explosion of document candidates and their display positions on the
 page. Therefore we propose a paradigm shift from the traditional viewpoint of solving a ranking problem to a direct slate generation framework. In this paper, we introduce List Conditional Variational Auto-Encoders (ListCVAE),
 which learn the joint distribution of documents on the slate conditioned
 on user responses, and directly generate full slates. Experiments on simulated
 and real-world data show that List-CVAE outperforms greedy ranking methods
 consistently on various scales of documents corpora. Recommender systems modeling is an important machine learning area in the IT industry, powering online advertisement, social networks and various content recommendation services BID0 Lu et al., 2015) . In the context of document recommendation, its aim is to generate and display an ordered list of "documents" to users (called a "slate" in BID2 ; BID3 ), based on both user preferences and documents content. For large scale recommender systems, a common scalable approach at inference time is to first select a small subset of candidate documents S out of the entire document pool D. This step is called "candidate generation". Then a function approximator such as a neural network (e.g., a Multi-Layer Perceptron (MLP)) called the "ranking model" is used to predict probabilities of user engagements for each document in the small subset S and greedily generates a slate by sorting the top documents from S based on estimated prediction scores BID4 . This two-step process is widely popular to solve large scale recommendation problems due to its scalability and fast inference at serving time. The candidate generation step can decrease the number of candidates from millions to hundreds or less, effectively dealing with scalability when faced with a large corpus of documents D. Since |S| is much smaller than |D|, the ranking model can be reasonably complicated without increasing latency.However, there are two main problems with this approach. First the candidate generation and the ranking models are not trained jointly, which can lead to having candidates in S that are not the highest scoring documents of the ranking model. Second and most importantly, the greedy ranking method suffers from numerous biases that come with the visual presentation of the slate and context in which documents are presented, both at training and serving time. For example, there exists positional biases caused by users paying more attention to prominent slate positions BID5 , and contextual biases, due to interactions between documents presented together in the same slate, such as competition and complementarity, relative attractiveness, etc. .In this paper, we propose a paradigm shift from the traditional viewpoint of solving a ranking problem to a direct slate generation framework. We consider a slate "optimal" when it maximizes some type of user engagement feedback, a typical desired scenario in recommender systems. For example, given a database of song tracks, the optimal slate can be an ordered list (in time or space) of k songs such that the user ideally likes every song in that list. Another example considers news articles, the optimal slate has k ordered articles such that every article is read by the user. In general, optimality can be defined as a desired user response vector on the slate and the proposed model should be agnostic to these problem-specific definitions. Solving the slate recommendation problem by direct slate generation differs from ranking in that first, the entire slate is used as a training example instead of single documents, preserving numerous biases encoded into the slate that might influence user responses. Secondly, it does not assume that more relevant documents should necessarily be put in earlier positions in the slate at serving time. Our model directly generates slates, taking into account all the relevant biases learned through training.In this paper, we apply Conditional Variational Auto-Encoders (CVAEs) BID7 BID8 to model the distributions of all documents in the same slate conditioned on the user response. All documents in a slate along with their positional, contextual biases are jointly encoded into the latent space, which is then sampled and combined with desired conditioning for direct slate generation, i.e. sampling from the learned conditional joint distribution. Therefore, the model first learns which slates give which type of responses and then directly generates similar slates given a desired response vector as the conditioning at inference time. We call our proposed model List-CVAE. The key contributions of our work are:1. To the best of our knowledge, this is the first model that provides a conditional generative modeling framework for slate recommendation by direct generation. It does not necessarily require a candidate generator at inference time and is flexible enough to work with any visual presentation of the slate as long as the ordering of display positions is fixed throughout training and inference times.2. To deal with the problem at scale, we introduce an architecture that uses pretrained document embeddings combined with a negatively downsampled k-head softmax layer within the List-CVAE model, where k is the slate size.The structure of this paper is the following. First we introduce related work using various CVAE-type models as well as other approaches to solve the slate generation problem. Next we introduce our List-CVAE modeling approach. The last part of the paper is devoted to experiments on both simulated and the real-world datasets.2 RELATED WORK Traditional matrix factorization techniques have been applied to recommender systems with success in modeling competitions such as the Netflix Prize BID10 . Later research emerged on using autoencoders to improve on the results of matrix factorization BID11 (CDAE, CDL). More recently several works use Boltzmann Machines BID13 and variants of VAE models in the Collaborative Filtering (CF) paradigm to model recommender systems BID14 BID15 BID16 ) (Collaborative VAE, JMVAE, CVAE-CF, JVAE-CF). See FIG0 for model structure comparisons. In this paper, unless specified otherwise, the user features and any context are routinely considered part of the conditioning variables (in Appendix A Personalization Test, we test List-CVAE generating personalized slates for different users). These models have primarily focused on modeling individual document or pairs of documents in the slate and applying greedy ordering at inference time.Our model is also using a VAE type structure and in particular, is closely related to the Joint Multimodel Variational Auto-Encoder (JMVAE) architecture FIG0 ). However, we use whole slates as input instead of single documents, and directly generate slates instead of using greedy ranking by prediction scores.Other relevant work from the Information Retrieval (IR) literature are listwise ranking methods BID17 BID18 BID19 BID20 BID21 . These methods use listwise loss functions that take the contexts and positions of training examples into account. However, they eventually assign a prediction score for each document and greedily rank them at inference time.In the Reinforcement Learning (RL) literature, BID3 view the whole slates as actions and use a deterministic policy gradient update to learn a policy that generates these actions, given concatenated document features as input.Finally, the framework proposed by BID22 predicts user engagement for document and position pairs. It optimizes whole page layouts at inference time but may suffer from poor scalability due to the combinatorial explosion of all possible document position pairs. The List-CVAE model moves away from the conventional greedy ranking paradigm, and provides the first conditional generative modeling framework that approaches slate recommendation problem using direct slate generation. By modeling the conditional probability distribution of documents in a slate directly, this approach not only automatically picks up the positional and contextual biases between documents at both training and inference time, but also gracefully avoids the problem of combinatorial explosion of possible slates when the candidate set is large. The framework is flexible and can incorporate different types of conditional generative models. In this paper we showed its superior performance over popular greedy and auto-regressive baseline models with a conditional VAE model.In addition, the List-CVAE model has good scalability. We designed an architecture that uses pretrained document embeddings combined with a negatively downsampled k-head softmax layer that greatly speeds up the training, scaling easily to millions of documents.
We used a CVAE type model structure to learn to directly generate slates/whole pages for recommendation systems.
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