Well, I am not sure how you flip the position, since it matters who is on the move.
-Joseph On 10 December 2011 16:17, Mark Higgins <migg...@gmail.com> wrote: > I've been playing around a bit with neural networks for backgammon and found > something interesting, and want to see whether this is already part of gnubg. > > Assume a Tesauro-style network with the usual inputs, and some number of > hidden nodes. And for simplicity, just one output representing the > probability of win. > > If I take a given board and translate the position into the inputs and then > evaluate the network, it gives me a probability of win. If I then flip the > board's perspective (ie white vs black) and do the same, I get another > probability of win. Those two probabilities should sum to 1, since one or the > other player must win (or equivalently, the probability of white winning = > probability of black losing = 1 - probability of black winning). > > But that constraint isn't satisfied with the usual TD setup. > > If however you make a few assumptions: > > * Hidden layer nodes don't include bias weight. > * Hidden->input weights have a specific symmetry: weight of the i'th hidden > node vs the j'th input node = w(i,j) = -w(i,j*), where j* is the index of the > other player's corresponding position. > * Output layer node doesn't include a bias weight. > > Then you can show that, for each set of output->hidden node weights, those > weights sum to zero, the flip-the-perspective constraint is satisfied. > > This seems to reduce the number of weights by about half, since you need only > half the middle weights. The network should be more accurate since a known > symmetry is respected, and should converge quicker since there are fewer > parameters to optimize. > > You can generalize to a bias weight on the output node; in that case, the > constraint is on the bias weight that it = -1/2 sum( output->hidden node > weights ). > > You can generalize as well to including a "gammon win" output node. In this > case there are no constraints on the output->hidden node weights, but the > probability of a gammon loss can be calculated from the probability of a > gammon win weights, and you don't need to explicitly include an output node > for the gammon loss. > > I googled around a fair bit but couldn't figure out whether this is well > known or already included somewhere in gnubg. I took a look through eval.c > but it's a bit daunting. :) Is there documentation somewhere that I've just > not found? > > > > _______________________________________________ > Bug-gnubg mailing list > Bug-gnubg@gnu.org > https://lists.gnu.org/mailman/listinfo/bug-gnubg _______________________________________________ Bug-gnubg mailing list Bug-gnubg@gnu.org https://lists.gnu.org/mailman/listinfo/bug-gnubg