Arbitrary-length-output online classifiers

Prove an analogue of the polynomial error bound for online classifiers whose computable classification functions output strings of arbitrary length, rather than only single bits or strings of constant length.

Background

The main online-classification theorem establishes a polynomial bound for binary-valued classifiers and notes that a similar result can be obtained when the output strings have constant length. The extension to classifiers producing outputs of unrestricted length is not established, and the authors explicitly state that they do not know how to prove it.