Is it possible to calculate gradient of a filter applied on the objects (that censor them)?

I want to find an optimal censoring function, that removes objects from a given set, as to maximise the set’s quality.

Suppose I am given a data set consisting of N objects, each is represented by a fixed number of numerical features.

I have a data quality function, that acts on the whole data set, and is differentiable with respect to all objects’ features. The function has no parameters.

I also have a second, censoring function which I want to train, that acts on a single object and returns a value that represents the relevance of the object to the data set. The function is parametrized and is differentiable wrt the object’s all features and its parameters.

I want to find optimal values of the parameters of the censoring function, so it filters out the objects from the data in such a way as it maximises the data quality function.

Of course, I can use non-gradient methods, such as genetic algorithms, but I ask about the application of a gradient descent method. I can’t simply compute the derrivative of the data quality function wrt parameters, because the relationship is discrete. But maybe there is a way to re-phrase the problem in such a way, that it becomes continuous.