CSE DSI Machine Learning Seminar with Ismail Alkhouri (LANL & UMich)

Differentiable Combinatorial Optimization at Scale

Many real-world decision-making problems can be formulated as large-scale combinatorial optimization (CO) problems. While integer programming and classical heuristics remain effective in many regimes, they often struggle to scale to very large problem instances. This talk explores a class of differentiable approaches to CO that relax discrete problems into continuous formulations optimized using projected gradient-based methods. We show that these relaxations lead to inherently non-convex landscapes and provide a characterization of their stationary and fixed points. Motivated by these insights, we introduce GPU-based parallelization strategies to improve exploration, enabling gradient-based optimizers to scale to large problem sizes. Using the Maximum Independent Set and Maximum Cut problems as case studies, we empirically examine when and why differentiable methods can outperform classical heuristics, where they fail, and how their exploration behavior can be further improved. The talk emphasizes how understanding the optimization landscape of relaxed combinatorial objectives informs the design of scalable and effective differentiable solvers.

Ismail Alkhouri is a Research Scientist III in the XCP Division at Los Alamos National Laboratory (LANL), hosted at Michigan SPARC, and a Research Scholar at the Michigan Institute for Computational Discovery and Engineering (MICDE) at the University of Michigan. He received his Ph.D. in Electrical and Computer Engineering from the University of Central Florida in 2023, during which he was a research intern in the Information Directorate at the Air Force Research Laboratory. Prior to joining LANL, he was a Research Scientist supporting the Information Innovation Office at DARPA. Before that, he was a postdoctoral research associate in the Computational Mathematics, Science, and Engineering (CMSE) Department at Michigan State University and in the Electrical Engineering and Computer Science Department at the University of Michigan. His research interests span generative models for inverse problems, differentiable approaches to combinatorial optimization, and robust machine learning. In 2025, he was recognized with the Conference on Parsimony and Learning (CPAL) Rising Stars Award and the CMSE Alumni Outstanding Research Award.