[Paper Review] GCOMB: Learning Budget-constrained Combinatorial Algorithms over Billion-sized Graphs

Sahil Manchanda, Akash Mittal+4 more|arXiv (Cornell University)|Mar 8, 2019

Advanced Graph Neural Networks22 citations

TL;DR

GCOMB proposes a scalable, budget-constrained framework for learning combinatorial algorithms on billion-sized graphs using a Graph Convolutional Network (GCN) with a probabilistic greedy mechanism and a Q-learning framework enhanced by importance sampling. It achieves 100x speedup over state-of-the-art methods while maintaining comparable solution quality, and 150x speedup on Influence Maximization compared to IMM.

ABSTRACT

There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node. To further facilitate the combinatorial nature of the problem, GCOMB utilizes a Q-learning framework, which is made efficient through importance sampling. We perform extensive experiments on real graphs to benchmark the efficiency and efficacy of GCOMB. Our results establish that GCOMB is 100 times faster and marginally better in quality than state-of-the-art algorithms for learning combinatorial algorithms. Additionally, a case-study on the practical combinatorial problem of Influence Maximization (IM) shows GCOMB is 150 times faster than the specialized IM algorithm IMM with similar quality.

Motivation & Objective

• To address the scalability gap in learning combinatorial algorithms for billion-sized graphs.
• To incorporate budget constraints into machine learning-based combinatorial optimization, which is critical for real-world applications.
• To develop a framework that maintains high solution quality while drastically improving inference speed.
• To evaluate the framework on real-world graphs and practical problems like Influence Maximization.

Proposed method

• GCOMB employs a Graph Convolutional Network (GCN) to predict node quality using a novel probabilistic greedy mechanism.
• It integrates a Q-learning framework to model the sequential decision-making process inherent in combinatorial selection.
• Importance sampling is applied to accelerate Q-learning training, improving efficiency without sacrificing learning quality.
• The framework jointly optimizes node selection under budget constraints, ensuring feasible and high-quality solutions.
• The training pipeline combines differentiable GCN prediction with reinforcement learning to refine selection policies.

Experimental results

Research questions

• RQ1 Can a machine learning framework effectively scale to billion-sized graphs for combinatorial optimization under budget constraints?
• RQ2 How does the integration of probabilistic greedy node scoring and Q-learning improve solution quality and training efficiency?
• RQ3 To what extent does GCOMB outperform existing learning-based and specialized algorithms in speed and solution quality?
• RQ4 Can GCOMB generalize to real-world combinatorial problems such as Influence Maximization?

Key findings

• GCOMB achieves a 100x speedup over state-of-the-art learning-based combinatorial algorithms on billion-sized graphs.
• On the Influence Maximization problem, GCOMB is 150x faster than the specialized IMM algorithm while maintaining similar solution quality.
• The framework maintains high solution quality, with marginal degradation compared to the best-performing baselines.
• The use of importance sampling in Q-learning significantly improves training efficiency, enabling scalability to large graphs.
• The probabilistic greedy mechanism in GCN provides stable and effective node quality estimation for combinatorial selection.