Appendix A1 Two Algorithms in Literature

The two algorithm discussed in Section 5.1 are Algorithm 2 and Algorithm 3. See Theorem 2.14.19 in [28]. It denotes the decision variables we obtain with a dual price p. 's while the second one comes from the feasibility Finally, we complete the proof with the help of the above three results. 's are specified according to Algorithm 1. Then R For the first part of (8), we can apply Proposition 1. Meanwhile, the analyses of the second part takes a similar form as the previous stochastic input model. Thus, we complete the proof for the regret.