Calculating optimal path(s) to increase probability of a classification I have trained several classifiers using Python's scikit-learn which are fairly accurate when applied on a test set at identifying different classes with a standardized set of input features. These different classifiers provide a certain probability for the classification.

The input features are controllable physical parameters that I am measuring (e.g. temperature, volume) which intricately influence an output which can essentially be either 1 or 0 (and others in mutli-class cases). I can already do basic identification, but what I am curious about is: given an initial feature vector starting in class 0, are there known methods to find the optimal ways to change my input features so as to increase my probability of going into class 1? The input feature space has a high number of dimensions, and there may be certain constraints on the inputs (e.g. temperature cannot exceed a certain value if volume is kept at a particular value).
This is a multivariate optimisation problem. You have a function f(X) that returns an output that you want to maximise - Maximising the probability of belonging to class. That function f(X) is just your model. 

You also mention "constraints", and again this is standard constrained optimisation territory. 

The problem itself may be hard to solve, but the framework seems to be that. 

Have a look at scipy optimise here