Position Paper: Incremental Search Algorithms Considered Poorly Understood

Incremental search algorithms, such as D* Lite, reuse information from previous searches to speed up the current search and can thus solve sequences of similar search problems faster than Repeated A*, which performs repeated A* searches. In this position paper, we study goal-directed navigation in initially unknown terrain and point out that it is currently not well understood when D* Lite runs faster than Repeated A*. In general, it appears that Repeated A* runs faster than D* Lite for easy navigation problems (where the agent reaches the goal with only a small number of searches), which means that it runs faster than D* Lite quite often in practice. We draw two conclusions, namely that incremental search algorithms need to be evaluated in more diverse testbeds to improve our understanding of their properties and that they can be improved to be more competitive for easy navigation problems. We study goal-directed navigation with the freespace assumption in initially unknown terrain, as needed in robotics and video games. The terrain is discretized into a grid of known dimensions. The agent does not know initially which cells are blocked but always observes the blockage status of the neighboring cells of its current cell and adds them to its map. It can then move to any unblocked neighboring cell. In this paper, the agent moves to a goal cell with given coordinates using the following navigation strategy: It finds a shortest (unblocked) path from its current cell to the goal cell. If such a path does not exist, it stops unsuccessfully. Otherwise, it follows the path until it either reaches the goal cell, in which case it stops successfully, or observes the path to be blocked, in which case it repeats the process. The agent thus needs to solve a sequence of similar search problems fast. Incremental search algorithms, such as D* Lite (Koenig and Likhachev 2005), reuse information from previous searches to speed up the current search. We claim that it is currently not well understood when D* Lite runs faster ∗Our research was supported by NSF, ARO and ONR grants to Sven Koenig (while he served at NSF) and a Fondecyt grant to Jorge Baier. Copyright c © 2012, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. than Repeated Forward A*.1 For example, it appears that Repeated Forward A* runs faster than D* Lite in many cases, typically for easy navigation problems where the agent observes its path to be blocked only a small number of times and thus performs only a small number of searches before it reaches the goal cell (or discovers that this is impossible). Examples are gridworlds where the start and goal cells are close to each other or where the h-values are not misleading (including where only a small number of cells are blocked). The reason appears to be the following: D* Lite has the advantage that it typically expands fewer cells than Repeated Backward A* after the first search since it reuses information from previous searches. However, D* Lite has the disadvantage that Repeated Backward A* typically expands more cells during the first searches than Repeated Forward A* during the first searches. D* Lite also expands cells more slowly than Repeated (Forward or Backward) A*. This means that the first search of D* Lite typically runs more slowly than the first search of Repeated Forward A*, an effect that becomes the more pronounced the further apart the start and goal cells are. If the number of subsequent searches needed for the agent to reach the goal cell is small then typically D* Lite runs more slowly than Repeated Forward A*. Repeated Forward A* performs repeated A* searches from the current cell of the agent to the goal cell and typically expands fewer cells than Repeated Backward A* during the first searches and thus runs faster, see (Koenig and Likhachev 2005) for an explanation. We use a version of Repeated Forward A* that finds a shortest path whenever the agent observes a blocked cell on its path (as most evaluations do), different from the previous evaluation in (Koenig and Likhachev 2005) where it finds a shortest path whenever the agent observes any blocked cell. D* Lite is a version of Repeated Backward A* that reuses information from previous searches. We use a version of D* Lite that breaks ties among cells with the same f-value in favor of smaller g-values since it typically runs faster than a version of D* Lite that breaks ties in the opposite direction because it a) expands more cells during the first search but fewer cells during subsequent searches and b) expands cells faster since its f-values are pairs rather than triples. 159 Proceedings of the Fifth Annual Symposium on Combinatorial Search