Several goal-oriented problems in the real-world can be naturally expressed as Stochastic Shortest Path problems (SSPs). However, the computational complexity of solving SSPs makes nding solutions to even moderately sized problems intractable. State-of-the-art SSP solvers are unable to learn generalized solutions or policies that would solve multiple problem instances with different object names and/or quantities. This paper presents an approach for learning Generalized Policy Automata (GPAs): non-deterministic partial policies that can be used to catalyze the solution process. GPAs are learned using relational, feature-based abstractions, which makes them applicable on broad classes of related problems with different object names and quantities. Theoretical analysis of this approach shows that it guarantees completeness and hierarchical optimality. Empirical analysis shows that this approach effectively learns broadly applicable policy knowledge in a few-shot fashion and signicantly outperforms state-of-the-art SSP solvers on test problems whose object counts are far greater than those used during training.

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.