Policies that Generalize: Solving Many Planning Problems with the Same Policy

We establish conditions under which memoryless policies and finite-state controllers that solve one partially observable non-deterministic problem (PONDP) generalize to other problems; namely, problems that have a similar structure and share the same action and observation space. This is relevant to generalized planning where plans that work for many problems are sought, and to transfer learning where knowledge gained in the solution of one problem is to be used on related problems. We use a logical setting where uncertainty is represented by sets of states and the goal is to be achieved with certainty. While this gives us crisp notions of solution policies and generalization, the account also applies to probabilistic PONDs, i.e., Goal POMDPs.