  In an online decision problem, one makes decisions often with a pool of
decision sequence called experts but without knowledge of the future. After
each step, one pays a cost based on the decision and observed rate. One
reasonal goal would be to perform as well as the best expert in the pool. The
modern and well-known way to attain this goal is the algorithm of exponential
weighting. However, recently, another algorithm called follow the perturbed
leader is developed and achieved about the same performance. In our work, we
first show the properties shared in common by the two algorithms which explain
the similarities on the performance. Next we will show that for a specific
perturbation, the two algorithms are identical. Finally, we show with some
examples that follow-the-leader style algorithms extend naturally to a large
class of structured online problems for which the exponential algorithms are
inefficient.
