Parallel and Mini-Batch Stable Matching for Large-Scale Reciprocal Recommender Systems

TL;DR

This work recasts stable matching for two-sided reciprocal recommender systems as an entropy-regularized optimal transport problem under transferable utility, enabling both high match quality and computational efficiency. It introduces parallel batch IPFP and online mini-batch IPFP to scale to up to a million users, leveraging a matrix–vector formulation with $A=\exp(\boldsymbol{\Phi}/(2\beta))$ and a factorized preference model for memory efficiency. The experiments on real and synthetic data demonstrate superior expected matches and solid scalability on CPU/GPU hardware, with memory usage that scales linearly and practical feasibility for large-scale platforms. The proposed approach offers a principled, scalable framework for maximizing total matches in large two-sided markets while preserving stability and fairness considerations inherent in TU-based matching.

Abstract

Reciprocal recommender systems (RRSs) are crucial in online two-sided matching platforms, such as online job or dating markets, as they need to consider the preferences of both sides of the match. The concentration of recommendations to a subset of users on these platforms undermines their match opportunities and reduces the total number of matches. To maximize the total number of expected matches among market participants, stable matching theory with transferable utility has been applied to RRSs. However, computational complexity and memory efficiency quadratically increase with the number of users, making it difficult to implement stable matching algorithms for several users. In this study, we propose novel methods using parallel and mini-batch computations for reciprocal recommendation models to improve the computational time and space efficiency of the optimization process for stable matching. Experiments on both real and synthetic data confirmed that our stable matching theory-based RRS increased the computation speed and enabled tractable large-scale data processing of up to one million samples with a single graphics processing unit graphics board, without losing the match count.

Figures (7)

• Figure 1: We propose a fast and memory-efficient solution to the TU matching problem, by viewing it as an optimal transport problem with transport costs associated with the inner product of the preference factor vectors.
• Figure 2: Our Mini-batch IPFP update keeps only a part of the matrices in memory during the update step, achieving parallel computation and memory efficiency.
• Figure 3: Results of Libimseti data experiments. The market size is 500 men and 500 women, and the examination function is $v(k) = 1 / \exp(k-1)$.
• Figure 4: Synthetic data experiment results at various crowding parameter levels. The market size is 500 jobs and 1000 candidates, and the examination function is $v(k) = 1 / \exp(k-1)$. When following the IPFP-based recommendation policy, the expected number of matches remains higher than the baseline methods as crowding parameters increase. For mini-batch IPFP, the number of matches slightly decreases because the preference matrix is approximated using the product of factor vectors.
• Figure 5: Calculation time (left) and memory usage (right) of batch and mini-batch IPFP with varying data size values. The average calculation times span over 100 iterations. Memory usage is measured on CPU memory for (a) and (c) and GPU memory for (b) and (d).