Author: rasjid chan
Date: 01:27:23 04/30/04
The Secret of the Commercial Chess Programmers IMNSHO. Omid mentioned Falcon reached 2600 after improvements in search and now he runs out of ideas to push search further and had to try to improve on his eval. Again eval would reach a barrier as most programs with 2600 has a very good eval and the eval curve again shows diminishing returns for code-increase / additional factors. The only way is to be able to have a vertical upward displacement for this eval-curve which is basically logarithmic - it may be +100 elo by just using the correctly tuned weights. The Deep Blue team mentioned they used MLR and since it can be done, it means it should not be too difficult as MLR itself is not very high mathematics. I used MLR before and has a not-yet-complete idea of using it to tune weights. The requirement is we need a collection of say 100 drawn game-files, the more the bettter as reading and applying eval() at all nodes for a 1000 games files may just take a second more. MLR tuning is logically based and it should not be too bad, at least we have some indications, but again we may not know it could be the BEST way to do weights tuning. Also it has a very high return if it works. It is a one time investment and once the tuner is written and we keep the 100 game-files, it could be re-used anytime we change our eval(), we only need 10 mins to do a rerun and we have all the weights re-tuned and we never need to worry too much what weights we assign when we add a new factor. The following is what I arrive at on first thought, it may be triple dumb! MLR is about finding a set of constants c0,c1,c2... for Y = c0 + c1*X1 + c2*X2 + ..... As I have not think it through completely, others may be able to complete the picture and let's see if it can be done easily. MLR requires us to collect a set of table data : per row: Y , X1, X2, X3,...., Xn a row/more is added to the table after applying our tuner to list thru the game-files and making the moves and apply score = eval() to the "neutral nodes". scheme 1:- Y is the should-be-near-zero score. Xn is our current weights used. scheme 2 - a "dumb" improvement :- Instead of using Xn we use del_Xn,the change in Xn alone(when only Xn is allowed to change) needed to make score == zero. After computing all del_Xn, we use Y = score = eval() using Xn + del_Xn instead of Xn. This may be better as weights not activated in certain nodes will have del_Xn = 0; Is this scheme ok ? Also in general for MLR, Y and Xn in should be scaled using a weighted average. Most common weights may vary about a certain mean value. Nodes should also be weighted, the nodes that eval() to far-from- zero are given less emphasis/weights/rows as the games are supposed to be drawn games. After running MLR, we obtain solution to c0,c1,c2... etc and this enables us to compute the optimal change needed to our weights. The correlation coefficient R2 from MLR may indicate how reliable the proposed changes is, or it may throw some lights on the quality of our eval(), etc. Also recording how often a factor is activated on average can let us decide if it may be discarded or used with a more conservative weight. MLR may also give us other indications when we may know certain factors are not important/or unstable when the tuned weights indicate an exceptionally high change needed, ie the weight or the factor itself may be suspect and should to be discarded. Should I do it now when my program is at 1900 ? Rasjid
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