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Also some deep enough model can learn how surfers (without flattening) "surf" hits, just like networks like "Deep Interest Network" used in CTR that learns how users' interest change over time. However our current use of KNN allows nothing like this. Maybe some end-to-end approach exists for robocode scenario.

My past experiments (shallow NN that does online-learning without pre-training) with end-to-end approach didn't yield anything interesting though.

Yeah, I also tried a purely NN gun and didn't get great results. You can train a NN offline to really high accuracy against random movement bots, but online it's much harder because data isn't iid.