Detecting Unsolvability Based on Separating Functions

While the unsolvability IPC sparked a multitude of planners proficient in detecting unsolvable planning tasks, there are gaps where concise unsolvability arguments are known but no existing planner can capture them without prohibitive computational effort. One such example is the sliding tiles puzzle, where solvability can be decided in polynomial time with a parity argument. We introduce separating functions, which can prove that one state is unreachable from another, and show under what conditions a potential function over any nonzero ring is a separating function. We prove that we can compactly encode these conditions for potential functions over features that are pairs, and show in which cases we can efficiently synthesize functions satisfying these conditions. We experimentally evaluate a domain-independent algorithm that successfully synthesizes such separating functions from PDDL representations of the sliding tiles puzzle, the Lights Out puzzle, and Peg Solitaire

Avoiding Dead Ends in Real-Time Heuristic Search

Many systems, such as mobile robots, need to be controlled in real time. Real-time heuristic search is a popular on-line planning paradigm that supports concurrent planning and execution. However,existing methods do not incorporate a notion of safety and we show that they can perform poorly in domains that contain dead-end states from which a goal cannot be reached. We introduce new real-time heuristic search methods that can guarantee safety if the domain obeys certain properties. We test these new methods on two different simulated domains that contain dead ends, one that obeys the properties and one that does not. We find that empirically the new methods provide good performance. We hope this work encourages further efforts to widen the applicability of real-time planning

Learning and planning in videogames via task decomposition

Artificial intelligence (AI) methods have come a long way in tabletop games, with computer programs having now surpassed human experts in the challenging games of chess, Go and heads-up no-limit Texas hold'em. However, a significant simplifying factor in these games is that individual decisions have a relatively large impact on the state of the game. The real world, however, is granular. Human beings are continually presented with new information and are faced with making a multitude of tiny decisions every second. Viewed in these terms, feedback is often sparse, meaning that it only arrives after one has made a great number of decisions. Moreover, in many real-world problems there is a continuous range of actions to choose from, and attaining meaningful feedback from the environment often requires a strong degree of action coordination. Videogames, in which players must likewise contend with granular time scales and continuous action spaces, are in this sense a better proxy for real-world problems, and have thus become regarded by many as the new frontier in games AI. Seemingly, the way in which human players approach granular decision-making in videogames is by decomposing complex tasks into high-level subproblems, thereby allowing them to focus on the "big picture". For example, in Super Mario World, human players seem to look ahead in extended steps, such as climbing a vine or jumping over a pit, rather than planning one frame at a time. Currently though, this type of reasoning does not come easily to machines, leaving many open research problems related to task decomposition. This thesis focuses on three such problems in particular: (1) The challenge of learning subgoals autonomously, so as to lessen the issue of sparse feedback. (2) The challenge of combining discrete planning techniques with extended actions whose durations and effects on the environment are uncertain. (3) The questions of when and why it is beneficial to reason over high-level continuous control variables, such as the velocity of a player-controlled ship, rather than over the most low-level actions available. We address these problems via new algorithms and novel experimental design, demonstrating empirically that our algorithms are more efficient than strong baselines that do not leverage task decomposition, and yielding insight into the types of environment where task decomposition is likely to be beneficial