Before revision:  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.
After revision:  this is motivated bymany applications , 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 and widely applicable smoothing framework based on randomization.