Instructor : Nikhil Bansal Scribe : Yiqun Chen 1 The general MWU setting

We can view the prediction problem considered previously as the following: We have m experts and we maintain a vector pt (probability distribution) over the experts and at each round nature reveals loss `t ∈ {0, 1}n. We incur expected loss pt · `t and therefore cumulative loss ∑T t=1 pt· `t. Moreover, in randomized weighted majority we set wi(t+1) = wi(t)(1− ) if i makes an mistake and we choose expert i with probability pi(t+ 1) = wi(t+1) ( ∑ i′ wi′ (t+1)) . We showed that