Appendix A Discretization based algorithm

Recall that C ⊂ R is contained in a ball of radius R. A standard greedy construction gives an r-discretization of size at most (3R/r) [Balcan et al., 2018a]. Given the dispersion parameter β, a natural choice is to use a T−β-discretization as in Algorithm 1. Theorem 4. Let Rfinite(T, s,N) denote the s-shifted regret for the finite experts problem on N experts, for the algorithm used in step 2 of Algorithm 1. Then Algorithm 1 enjoys s-shifted regret RC(T, s) which satisfies