AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-20
Distributional Lifting for Discrete Optimization
The paper proposes a framework that turns discrete optimization into continuous optimization over parameterized probability distributions. It shows that several separately developed methods, including the cross-entropy method and the quantum approximate optimization algorithm, share this distributional structure. A unified algorithm based on batched sampling and stochastic gradient updates is presented, and it is applied to three case studies: multidimensional knapsack, three-dimensional assignment, and a stochastic mixed-integer location-allocation problem.