Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?

TL;DR

This paper introduces a neural model with expressive message passing and energy-based training that generalizes across multiple graph combinatorial optimization tasks, leveraging computational reducibility for transfer learning.

Contribution

It proposes a novel GCON-based model and transfer strategies inspired by computational reducibility to improve generalization across CO tasks.

Findings

High performance comparable to state-of-the-art on individual tasks

Effective transfer between MVC, MIS, MaxClique, and others

Pretraining accelerates convergence and prevents negative transfer

Abstract

A key challenge in deriving unified neural solvers for combinatorial optimization (CO) is efficient generalization of models between a given set of tasks to new tasks not used during the initial training process. To address it, we first establish a new model, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves high performance (often comparable with state-of-the-art results) across multiple CO tasks when trained individually on each task. We then leverage knowledge from the computational reducibility literature to propose pretraining and fine-tuning strategies that transfer effectively (a) between MVC, MIS and MaxClique, and (b) in a multi-task learning setting that additionally incorporates MaxCut, MDS and graph coloring. Additionally, in a leave-one-out, multi-task learning setting, we observe that pretraining on all but one task almost always leads to faster convergence on the remaining task when fine-tuning while avoiding negative transfer. Our findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with pretraining strategies that are informed by the polynomial reduction literature, thereby taking an important step towards enabling the development of foundational models for neural CO. We provide an open-source implementation of our work at https://github.com/semihcanturk/COPT-MT .