Is reinforcement learning the right approach for finding unknown functional relationship in this example?

Question

We have a machine learning problem as depicted in the following figure.

It has the following structure:

1. Data consists out of float values $a_i$, $n_i$, $X_i$, $Y_i$ and an outcome $O_i$ (0 or 1).

2. $X_i$ and $Y_i$ are decisive for $F_i$ and there is a functional relationship between $X_i$ and $Y_i$ and $F_i$ but we don't know the type of it and it might be very complex.

3. What we know is how $F_i$ needs to be postprocessed to find $G_i$, i.e. we calculate $H_i=f(F_i,n_i)$ and compare $H_i$ against $a_i$ which gives $G_i=1$ if $H_i>a_i$ and 0 otherwise.

4. What we want is the best agreement between all $G_i$ and $O_i$.

So to sum it up: We are interested in a neural network (or similar) that allows us to predict $F_j$ for a new dataset $X_j$ and $Y_j$, but we can only train using the booleans $G_i$ and we do not know or have any access to any training value $F_i$.

We thought about reinforcement learning, but I only heard of applications in action taking depending on a state (e.g. pacman).

Can you tell me if reinforcement learning might work on this or can you direct me to any other field in machine learning that might help here?

Answer 1

I think if you use a neural network classification and train your model using back-propagation your model would find the best value for Fj. Therefore for your test set with given new Xj and Yj values your trained model will predict the Gj.

This way you don't need and Fj values since your network will choose Fj value to predict the outcome which is either 0 or 1.

Reinforcement Learning is used for maximising the reward from the environment, so you can use a normal neural network for predicting the Gj values

hope it helped