With the advancement of deep learning, deep recommendation models have achieved remarkable improvements in recommendation accuracy. However, due to the large number of candidate items in practice and the high cost of preference computation, these methods still suffer from low recommendation efficiency. The recently proposed tree-based deep recommendation models alleviate the problem by directly learning tree structure and representations under the guidance of recommendation objectives. To guarantee the effectiveness of beam search for recommendation accuracy, these models strive to ensure that the tree adheres to the max-heap assumption, where a parent node's preference should be the maximum among its children's preferences. However, they employ a one-versus-all strategy, framing the training task as a series of independent binary classification objectives for each node, which limits their ability to fully satisfy the max-heap assumption. To this end, we propose a Deep Tree-based Retriever (DTR for short) for efficient recommendation. DTR frames the training task as a softmax-based multi-class classification over tree nodes at the same level, enabling explicit horizontal competition and more discriminative top-k selection among them, which mimics the beam search behavior during training. To mitigate the suboptimality induced by the labeling of non-leaf nodes, we propose a rectification method for the loss function, which further aligns with the max-heap assumption in expectation. As the number of tree nodes grows exponentially with the levels, we employ sampled softmax to approximate optimization and thereby enhance efficiency. Furthermore, we propose a tree-based sampling method to reduce the bias inherent in sampled softmax. Theoretical results reveal DTR's generalization capability, and both the rectification method and tree-based sampling contribute to improved generalization. The experiments are conducted on four real-world datasets, validating the effectiveness of the proposed method.

Vector retrieval focuses on finding the k-nearest neighbors from a bunch of data points, and is widely used in a diverse set of areas such as information retrieval and recommender system. The current state-of-the-art methods represented by HNSW usually generate indexes with a big memory footprint, restricting the scale of data they can handle, except resorting to a hybrid index with external storage. The space-partitioning learned indexes, which only occupy a small memory, have made great breakthroughs in recent years. However, these methods rely on a large amount of labeled data for supervised learning, so model complexity affects the generalization.

Vector quantization techniques, such as Product Quantization (PQ), play a vital role in approximate nearest neighbor search (ANNs) and maximum inner product search (MIPS) owing to their remarkable search and storage efficiency. However, the indexes in vector quantization cannot be trained together with the inference models since data indexing is not differentiable. To this end, differentiable vector quantization approaches, such as DiffPQ and DeepPQ, have been recently proposed, but existing methods have two drawbacks. First, they do not impose any constraints on codebooks, such that the resultant codebooks lack diversity, leading to limited retrieval performance. Second, since data indexing resorts to operator, differentiability is usually achieved by either relaxation or Straight-Through Estimation (STE), which leads to biased gradient and slow convergence. To address these problems, we propose a Differentiable Optimized Product Quantization method (DOPQ) and beyond in this paper. Particularly, each data is projected into multiple orthogonal spaces, to generate multiple views of data. Thus, each codebook is learned with one view of data, guaranteeing the diversity of codebooks. Moreover, instead of simple differentiable relaxation, DOPQ optimizes the loss based on direct loss minimization, significantly reducing the gradient bias problem. Finally, DOPQ is evaluated with seven datasets of both recommendation and image search tasks. Extensive experimental results show that DOPQ outperforms state-of-the-art baselines by a large margin.

We focus on Maximum Inner Product Search (MIPS), which is an essential problem in many machine learning communities. Given a query, MIPS finds the most similar items with the maximum inner products. Methods for Nearest Neighbor Search (NNS) which is usually defined on metric space do not exhibit the satisfactory performance for MIPS problem since inner product is a non-metric function. However, inner products exhibit many good properties compared with metric functions, such as avoiding vanishing and exploding gradients. As a result, inner product is widely used in many recommendation systems, which makes efficient Maximum Inner Product Search a key for speeding up many recommendation systems. Graph-based methods for NNS problem show the superiorities compared with other class methods. Each data point of the database is mapped to a node of the proximity graph. Nearest neighbor search in the database can be converted to route on the proximity graph to find the nearest neighbor for the query. This technique can be used to solve MIPS problem. Instead of searching the nearest neighbor for the query, we search the item with a maximum inner product with query on the proximity graph. In this article, we propose a reinforcement model to train an agent to search on the proximity graph automatically for MIPS problem if we lack the ground truths of training queries. If we know the ground truths of some training queries, our model can also utilize these ground truths by imitation learning to improve the agent’s searchability. By experiments, we can see that our proposed mode which combines reinforcement learning with imitation learning shows the superiorities over the state-of-the-art methods.

Recommender systems (RS) have to select the top-N items from a massive item set. For the sake of efficient recommendation, RS usually represents user and item as latent embeddings, and relies on approximate nearest neighbour search (ANNs) to retrieve the recommendation result. Despite the reduction of running time, the representation learning is independent of ANNs index construction; thus, the two operations can be incompatible, which results in potential loss of recommendation accuracy. To overcome the above problem, we propose the Recommender Forest (a.k.a., RecForest), which jointly learns latent embedding and index for efficient and high-fidelity recommendation. RecForest consists of multiple k-ary trees, each of which is a partition of the item set via hierarchical balanced clustering such that each item is uniquely represented by a path from the root to a leaf. Given such a data structure, an encoder-decoder based routing network is developed: it first encodes the context, i.e., user information, into hidden states; then, leveraging a transformer-based decoder, it identifies the top-N items via beam search. Compared with the existing methods, RecForest brings in the following advantages: 1) the false partition of the boundary items can be effectively alleviated by the use of multiple trees; 2) the routing operation becomes much more accurate thanks to the powerful transformer decoder; 3) the tree parameters are shared across different tree levels, making the index to be extremely memory-efficient. The experimental studies are performed on five popular recommendation datasets: with a significantly simplified training cost, RecForest outperforms competitive baseline approaches in terms of both recommendation accuracy and efficiency.

With the development of deep learning techniques, deep recommendation models also achieve remarkable improvements in terms of recommendation accuracy. However, due to the large number of candidate items in practice and the high cost of preference computation, these methods also suffer from low efficiency of recommendation. The recently proposed tree-based deep recommendation models alleviate the problem by directly learning tree structure and representations under the guidance of recommendation objectives. However, such models have two shortcomings. First, the max-heap assumption in the hierarchical tree, in which the preference for a parent node should be the maximum between the preferences for its children, is difficult to satisfy in their binary classification objectives. Second, the learned index only includes a single tree, which is different from the widely-used multiple trees index, providing an opportunity to improve the accuracy of recommendation.