I have been reading into Neural Networks with the aim of using them to optimize a multi objective cost function (aka finding Pareto fronts) which takes a long time to call.
The inputs are constrained to within a certain range of real numbers. Is the ONLY way a NN can help with this task is to come up with a computationally faster function to call to find an optimal solution or is there something more clever that I can do?
For example, can I teach the system using reverse data such that the objective function's output is my NN input and vice versa and try values of object output for a maxima/minima?
Best Answer
There are at least two problems with your proposed approach:
Neural Networks perform supervised learning - meaning that you will need existing examples of valid input-ouput pairs. In your case you will need several instances of input variables + correct values of your objective function to start training your network. But you just mentioned that your objective function takes a long time to call. So you have a "chicken and egg" problem.
Second, even if you did have these values provided by some sort of oracle, training a neural network is itself a difficult optimization problem. So you would simply be moving the difficulty of your optimization from the function call to the training of the neural net.