Eachofthebase neurons is labelled by a function from the base classH.

Additional notation For a matrix A Rd1 d2, A op is the operator norm (with respect to Euclidean norms), and A F istheFrobenius norm ofA. The main intuition behind the HMM considered in this paper comes from the correlation decay phenomenon ingraphicalmodel. Informally, we expect that there is one sign flip (i.e., Si = Si+1) per 1δ samples. To begin with the analysis of the estimator in Figure 2, the following lemma is a simple, yet key tool for the proof. It establishes the variance of the random gainS.

Inthissetting,all rewards drawn from an arm are independent and identically distributed.