Just a small tip which may ease the search for methods. The general term for "on the fly" learning is online learning [1]. The rest depends on your problem but

Just a small tip which may ease the search for methods. The general term for "on the fly" learning is online learning [1]. The rest depends on your problem but there are often online variants of offline methods, e.g. when you work with Gaussian process regressions [1]: http://en.wikipedia.org/wiki/Online_machine_learning http://en.wikipedia.org/wiki/Online_machine_learning