Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets
This addresses NP-hard combinatorial optimization problems for researchers and practitioners, offering an incremental improvement by applying GFlowNets to structured constraints.
The paper tackles combinatorial optimization problems by training conditional GFlowNets to sample high-quality solutions, demonstrating through experiments on various tasks that these policies efficiently find such solutions.
Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions. Our implementation is open-sourced at https://github.com/zdhNarsil/GFlowNet-CombOpt.