GuideCO: Training Objective-Guided Diffusion Solver with Imperfect Data for Combinatorial Optimization

Hui Yuan, Zhigang Hua, Zihao Li, Weilin Cong, Yan Xie, Rong Jin, Shuang Yang, Bo Long, Mengdi Wang

Keywords: combinatorial optimization, diffusion model, guidance

Abstract: Combinatorial optimization (CO) problems have widespread applications in science and engineering but they present significant computational challenges. Recent advancements in generative models, particularly diffusion models, have shown promise in bypassing traditional optimization solvers by directly generating near-optimal solutions. However, we observe an exponential scaling law between the optimality gap and the amount of training data needed for training diffusion-based solvers. Notably, the performance of existing diffusion solvers relies on both quantity and quality of training data: they perform well with abundant high quality training data labeled by exact or near-optimal solvers, while suffering when high-quality labels are scarce or unavailable. To address the challenge, we propose GuideCO, an objective-guided diffusion solver for combinatorial optimization, which can be trained on imperfectly labelled datasets. GuideCO is a two-stage generate-then-decode framework, featuring an objective-guided diffusion model that is further reinforced by classifier-free guidance for generating high-quality solutions on any given problem instance. Experiments demonstrate the improvements of GuideCO against baselines when trained on imperfect data, in a range of combinatorial optimization benchmark tasks such as TSP (Traveling Salesman Problem) and MIS (Maximum Independent Set).

Primary Area: optimization

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Submission Number: 8862