  We introduce the technique of generic chaining and majorizing measures for
controlling sequential Rademacher complexity. We relate majorizing measures to
the notion of fractional covering numbers, which we show to be dominated in
terms of sequential scale-sensitive dimensions in a horizon-independent way,
and, under additional complexity assumptions establish a tight control on
worst-case sequential Rademacher complexity in terms of the integral of
sequential scale-sensitive dimension. Finally, we establish a tight contraction
inequality for worst-case sequential Rademacher complexity. The above
constitutes the resolution of a number of outstanding open problems in
extending the classical theory of empirical processes to the sequential case,
and, in turn, establishes sharp results for online learning.
