ADI doesn't converge

[Ntiboroo1]

Hi,

I try to do my own implementation as a personal learning (I use keras, not pytorch).
As I understood value should ideally represent a "distance" from the goal state, like:

• for the solved cube, 0.
• for states which are neighbour of the solved state, 1.
• for states which are 2 distant from the solved state, 0.
• for states which are 3 distant from the solved state, -1.
• for states which are 4 distant from the solved state, -2.
  etc.

In my case sometimes the value is increasing the further the state really is from the solved state:

• for solved cube,0. (this is forced to be labeled as 0 all times, as in your solution)
• for neighbours, 1. (I manage to force this to be 1+V(solved state) )
• for 2 distant states, 2. (or an arbitrary value, more than 1)
• for 3 distant states, 3.
  etc.

The problem I think is that there will always be a state which is not in the training data, thus the above solution indeed has low squared error:
Take into account a chain in the training set (states that are neighbours and the "real, unknown" distance is increasing) with states S1, S2, S3...Sn (Here S1, ... Sn are in the training set, and the index measures the real distance, e.g. minimal rotations needed to solve the state).
V(S0) =0,V(S1)=1 |here the states fall apart| V(S2) = V(S3)-1=...=V(Sn)-1 = V(Sn+1)-1 is a good solution, since Sn+1 is not in the training set, thus V(Sn+1) could be anything (e.g. 10000).
Here V(S) is the value predicted by the Neural Net.

What am I missing? What makes the above solution invalid to converge to? It should be penalized somehow...

Thank you