Differentiable Greedy Algorithm for Monotone Submodular Maximization: Guarantees, Gradient Estimators, and Applications

Motivated by, e.g., sensitivity analysis and end-to-end learning, the demand for differentiable optimization algorithms has been increasing. This paper presents a theoretically guaranteed differentiable greedy algorithm for monotone submodular function maximization. We smooth the greedy algorithm via randomization, and prove that it almost recovers original approximation guarantees in expectation for the cases of cardinality and $\kappa$-extendible system constraints. We then present how to efficiently compute gradient estimators of any expected output-dependent quantities. We demonstrate the usefulness of our method by instantiating it for various applications.