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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?

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  • $\begingroup$ 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? $\endgroup$ – D.W.♦ Aug 17 '20 at 17:18
  • $\begingroup$ 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? $\endgroup$ – Fatemeh Aug 18 '20 at 8:35

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