  This paper addresses the complex issue of resource-constrained scheduling, an
NP-hard problem that spans critical areas including chip design and
high-performance computing. Traditional scheduling methods often stumble over
scalability and applicability challenges. We propose a novel approach using a
differentiable combinatorial scheduling framework, utilizing Gumbel-Softmax
differentiable sampling technique. This new technical allows for a fully
differentiable formulation of linear programming (LP) based scheduling,
extending its application to a broader range of LP formulations. To encode
inequality constraints for scheduling tasks, we introduce \textit{constrained
Gumbel Trick}, which adeptly encodes arbitrary inequality constraints.
Consequently, our method facilitates an efficient and scalable scheduling via
gradient descent without the need for training data. Comparative evaluations on
both synthetic and real-world benchmarks highlight our capability to
significantly improve the optimization efficiency of scheduling, surpassing
state-of-the-art solutions offered by commercial and open-source solvers such
as CPLEX, Gurobi, and CP-SAT in the majority of the designs.
