Research Group Stefanie Jegelka
Stefanie Jegelka
is a Humboldt Professor at TU Munich.
Her research is in algorithmic machine learning, and spans modeling, optimization algorithms, theory and applications. In particular, she has been working on exploiting mathematical structure for discrete and combinatorial machine learning problems, for robustness and for scaling machine learning algorithms.
Team members @MCML
Publications @MCML
Are Graph Neural Networks Optimal Approximation Algorithms?.
38th Conference on Neural Information Processing Systems (NeurIPS 2024). Vancouver, Canada, Dec 10-15, 2024. To be published. Preprint at arXiv. arXiv.
Abstract
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP). Concretely, we prove that polynomial-sized message-passing algorithms can represent the most powerful polynomial time algorithms for Max Constraint Satisfaction Problems assuming the Unique Games Conjecture. We leverage this result to construct efficient graph neural network architectures, OptGNN, that obtain high-quality approximate solutions on landmark combinatorial optimization problems such as Max-Cut, Min-Vertex-Cover, and Max-3-SAT. Our approach achieves strong empirical results across a wide range of real-world and synthetic datasets against solvers and neural baselines. Finally, we take advantage of OptGNN's ability to capture convex relaxations to design an algorithm for producing bounds on the optimal solution from the learned embeddings of OptGNN.