The loss function of each expert in the expert advice problem(or any online learning problem) depends on the time($ t$ ) and expert advice at that time($ f_{t}(i)$ ). suppose in this problem, loss function depends on the previous prediction of the algorithm. $ $ l _{t} (i) = p_{1} p_{2} \cdots p_{t-1}f_{t}(i)$ $ such that $ p$ show prediction of algorithm.

Does the upper bound of regret change?