Constructing a strong heuristic function is a central problem in heuristic search. A common approach is to combine a number of heuristics by maximizing over the values from each. If a limit is placed on this number, then a subset selection problem arises. We treat this as an optimization problem, and proceed by translating a natural loss function into a submodular and monotonic utility function under which greedy selection is guaranteed to be near-optimal. We then extend this approach with a sampling scheme that retains provable optimality. Our empirical results show large improvements over existing methods, and give new insight into building heuristics for directed domains.

Real-time heuristic search algorithms obey a constant limit on planning time per move. Agents using these algorithms can execute each move as it is computed, suggesting a strong potential for application to real-time video-game AI. Recently, a breakthrough in real-time heuristic search performance was achieved through the use of case-based reasoning. In this framework, the agent optimally solves a set of problems and stores their solutions in a case base. Then, given any new problem, it seeks a similar case in the case base and uses its solution as an aid to solve the problem at hand. A number of ad hoc approaches to the case base formation problem have been proposed and empirically shown to perform well. In this paper, we investigate a theoretically driven approach to solving the problem. We mathematically relate properties of a case base to the suboptimality of the solutions it produces and subsequently develop an algorithm that addresses these properties directly. An empirical evaluation shows our new algorithm outperforms the existing state of the art on contemporary video-game pathfinding benchmarks.