Before revision:  We prove that the Triggering Probability Modulated (TPM) condition for CMAB still holds , and then utilize the property of competitive diffusion to introduce a new offline oracle, and discuss how to implement this new oracle in various cases.
After revision:  We provide a nontrivial proof showing that the Triggering Probability Modulated (TPM) condition for CMAB still holds , and then utilize the property of competitive diffusion to introduce a new offline oracle, and discuss how to implement this new oracle in various cases.