  We study the adversarial multi-armed bandit problem and create a completely
online algorithmic framework that is invariant under arbitrary translations and
scales of the arm losses. We study the expected performance of our algorithm
against a generic competition class, which makes it applicable for a wide
variety of problem scenarios. Our algorithm works from a universal prediction
perspective and the performance measure used is the expected regret against
arbitrary arm selection sequences, which is the difference between our losses
and a competing loss sequence. The competition class can be designed to include
fixed arm selections, switching bandits, contextual bandits, or any other
competition of interest. The sequences in the competition class are generally
determined by the specific application at hand and should be designed
accordingly. Our algorithm neither uses nor needs any preliminary information
about the loss sequences and is completely online. Its performance bounds are
the second order bounds in terms of sum of the squared losses, where any affine
transform of the losses has no effect on the normalized regret.
