  When dealing with time series with complex non-stationarities, low
retrospective regret on individual realizations is a more appropriate goal than
low prospective risk in expectation. Online learning algorithms provide
powerful guarantees of this form, and have often been proposed for use with
non-stationary processes because of their ability to switch between different
forecasters or ``experts''. However, existing methods assume that the set of
experts whose forecasts are to be combined are all given at the start, which is
not plausible when dealing with a genuinely historical or evolutionary system.
We show how to modify the ``fixed shares'' algorithm for tracking the best
expert to cope with a steadily growing set of experts, obtained by fitting new
models to new data as it becomes available, and obtain regret bounds for the
growing ensemble.
