# Does regret change when the loss function is dependent on the previous predictions?

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?

• Have you tried working through the standard proof to see if it breaks down in this setting? Have you tried to work through some simple examples? – D.W. Aug 17 '20 at 17:18
• I see the multiplicative weights update algorithm and proof it. but I like to know Does dependency does not affect the calculation or definition of regret? – Fatemeh Aug 18 '20 at 8:35