Before revision:  We analyze the algorithm in two different models, the stochastic input model and the random permutationmodel , with minimal  assumptions on the input of the LP . The algorithm achieves O\left(m n\right) expected regret under the stochastic input model and O\left((m+\log n)n\right) expected regret under the random permutation model, and it achieves O(m n) expected constraint violation under both models, where n is the number of decision variables and m is the number of constraints.
After revision:  We analyze the algorithm in two different models, the stochastic input model and the random permutationmodel , with minimal technical assumptions on the input of the LP . The algorithm achieves O\left(m n\right) expected regret under the stochastic input model and O\left((m+\log n)n\right) expected regret under the random permutation model, and it achieves O(m n) expected constraint violation under both models, where n is the number of decision variables and m is the number of constraints.