1. By "tune" I mean that I filter the evaluation function through a logistic that maps the evaluation to a game result (0...1, with 0=black wins, 1=white wins, 0.5=draw). The idea is pretty standard. I use f(x) = 1/(1+exp(-k*x)), with x the evaluation in pawn units and k a scaling constant (which happens to be 1 according to a monte-carlo best parameter estimate).
2. I use the test position set by Alexandru Mosoi (http://talkchess.com/forum/viewtopic.php?p=686204).
3. To fit the data, I use stochastic gradient descent with 1000 positions in each estimate for the gradient. I haven't tried anything more fancy, but I did first try the Simplex algorithm from GSL as an alternative. This works ok too.
4. In the evaluation, I have fixed the value of a pawn in the end game (VALUE_P_EG) at 256. This fixes the scale for the evaluation, which is otherwise arbitrary.
5. During tuning, evaluation parameters are treated as double-precision floating point numbers.
6. I started with 11 parameters to tune: piece values for N, B, R, Q in MG and EG, pawn value in MG and bishop pair bonus for MG and EG (this is in fact just the quadratic term in the material evaluation).
The initial parameters are
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MG EG P 0.80 1.00 N 3.25 3.50 B 3.25 3.50 R 4.50 5.50 Q 9.00 9.75 BB 0.00 0.00
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MG EG P 0.96 1.00 N 3.46 2.39 B 3.37 2.54 R 4.40 4.70 Q 8.79 9.29 BB 0.17 0.21
This makes me wonder if there's something I'm overlooking in how I've implemented my optimiser. What I'm wondering is whether anyone else has done a similar experiment with similar results? In particular, I would like to know if anyone has tried to match Alexandru Mosoi's dataset with just material and arrived at "correct" piece values that represent the data.