The wrong direction of Jensen's inequality is algorithmically right
Let đ be an algorithm with expected running time e^X, conditioned on the value of some random variable X. We construct an algorithm đ' with expected running time O(e^E[X]), that fully executes đ. In particular, an algorithm whose running time is a random variable T can be converted to one with expected running time O(e^E[ln T]), which is never worse than O(E[T]). No information about the distribution of X is required for the construction of đ'.
READ FULL TEXT