Due to the discrete nature of COMBO's search space, the implementation detail is slightly different. In contrast, in COMBO's combinatorial graphs, we have spray vertices. Using random vertices for exploration is similar to Spearmint.

Figure 1: Problem instance where perfect heuristic is not strictly optimally efficient with GBFS. However, the path (A, C,D, E) has cost 10 instead of 11 . Then h is a perfect ranking for GBFS on Γ. Proof. We carry the proof by induction with respect to the number of expanded states. Let's now make the induction step and assume the theorem holds for the first A 0 B 1 C 1 D 2 A 1 1 9 9 1 Figure 2: Problem instance where optimally efficient heuristic does not exists for GBFS.

Cascading bandits is a natural and popular model that frames the task of learning to rank from Bernoulli click feedback in a bandit setting.

To retrieve and recommend the most relevant items to users under response time limits, resorting to an efficient index structure is an effective and practical solution.