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If I understand correctly, for n firing waves w = {w1..wn}, LOOCV involves training the gun with w - {wi}, then test with wi, for all i. For knn guns, this means doing n “(k+1)nn” searches (then exclude wi from result), and for neural networks, this means feeding the network n(n-1) waves in total. Isn’t that costly for robocode? Or may there be some faster ways?

For KNN I think this is fine. I know personally I use a very fast kernel density function (square), so these kind of tests aren't expensive. That said, I haven't tried this technique yet. It might not work well due to other things we haven't spoken of yet.

Agreed though for NN, it is already pushing the limit of what can be processed in a single tick, so there is no way you can take 2x or 3x the processing power.

So do you mean only 2~3 waves need to be tested? I thought we need to iterate through every fired waves and do a knn search for each.