MGMatch: Fast Matchmaking with Nonlinear Objective and Constraints via Multimodal Deep Graph Learning

As a core problem of online games, matchmaking is to assign players into multiple teams to maximize their gaming experience. With the rapid development of game industry, it is increasingly difficulty to explicitly model players' experiences as linear functions. Instead, it is often modeled in a data-driven way by training a neural network. Meanwhile, complex rules must be satisfied to ensure the robustness of matchmaking, which are often described using logical operators. Therefore, matchmaking in practical scenarios is a challenging combinatorial optimization problem with nonlinear objective, linear constraints and logical constraints, which receives much less attention in previous research. In this paper, we propose a novel deep learning method for high-quality matchmaking in real-time. We first cast the problem as standard mixed-integer programming (MIP) by linearizing ReLU networks and logical constraints. Then, based on supervised learning, we design and train a multi-modal graph learning architecture to predict optimal solutions end-to-end from instance data, and solve a surrogate problem to efficiently obtain feasible solutions. Evaluation results on real industry datasets show that our method can deliver near-optimal solutions within 100ms.