We consider making outputs of the greedy algorithm for monotone submodular function maximization differentiable w.r.t. parameters of objective functions; this is motivated bymany applications , e.g., sensitivity analysis and end-to-end learning . Our contribution is a theoretically guaranteed and widely applicable smoothing framework based on randomization. We prove that our smoothed greedy algorithm almost recovers original approximation guarantees in expectation for the cases of cardinality and \kappa-extensible system constrains. We also show how to efficiently compute unbiased gradient estimators of any expected output-dependent quantities by sampling outputs . We demonstrate the utility and effectiveness of our framework by applying it to various situations including the aforementioned ones .
Motivated by , e.g., sensitivity analysis and end-to-end learning , the demand for differentiable optimization algorithms has been significantly increasing. In this paper, we establish a theoretically guaranteed versatile framework that makes the greedy algorithm for monotone submodular function maximization differentiable. 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-extensible system constrains. We also show how to efficiently compute unbiased gradient estimators of any expected output-dependent quantities . We demonstrate the usefulness of our framework by instantiating it for various applications .
R
We consider making outputs of the greedy algorithm for monotone submodular function maximization differentiable w.r.t. parameters of objective functions; this is motivated bymany applications
Motivated by
R
. Our contribution is
, the demand for differentiable optimization algorithms has been significantly increasing. In this paper, we establish
R
and widely applicable smoothing framework based on randomization. We prove that our smoothed greedy algorithm
versatile framework that makes the greedy algorithm for monotone submodular function maximization differentiable. We smooth the greedy algorithm via randomization, and prove that it
D
by sampling outputs
R
utility and effectiveness
usefulness
R
applying it to various situations including the aforementioned ones
instantiating it for various applications