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?