Best of Both Worlds

Abstract

Semi-Bandit Setting for t = 1, . . . , T The learner selects a combinatorial action Xt ∈ X , where X ⊂ {0, 1}. Simultaneously, environment selects a loss vector `t ∈ [−1, 1] The learner suffers the loss 〈Xt, `t〉 The learner observes the (semi-bandit) feedback ot = Xt ◦ `t ∈ [−1, 1], where ◦ is element-wise multiplication. It is easy to see that, when X = {e1, . . . , ed}, the problem reduces to the general MAB.