Silvan Sievers

Merge-and-shrink abstractions for classical planning : theory, strategies, and implementation

Classical planning is the problem of finding a sequence of deterministic actions in a state space that lead from an initial state to a state satisfying some goal condition. The dominant approach to optimally solve planning tasks is heuristic search, in particular A* search combined with an admissible heuristic. While there exist many different admissible heuristics, we focus on abstraction heuristics in this thesis, and in particular, on the well-established merge-and-shrink heuristics. Our main theoretical contribution is to provide a comprehensive description of the merge-and-shrink framework in terms of transformations of transition systems. Unlike previous accounts, our description is fully compositional, i.e. can be understood by understanding each transformation in isolation. In particular, in addition to the name-giving merge and shrink transformations, we also describe pruning and label reduction as such transformations. The latter is based on generalized label reduction, a new theory that removes all of the restrictions of the previous definition of label reduction. We study the four types of transformations in terms of desirable formal properties and explain how these properties transfer to heuristics being admissible and consistent or even perfect. We also describe an optimized implementation of the merge-and-shrink framework that substantially improves the efficiency compared to previous implementations. Furthermore, we investigate the expressive power of merge-and-shrink abstractions by analyzing factored mappings, the data structure they use for representing functions. In particular, we show that there exist certain families of functions that can be compactly represented by so-called non-linear factored mappings but not by linear ones. On the practical side, we contribute several non-linear merge strategies to the merge-and-shrink toolbox. In particular, we adapt a merge strategy from model checking to planning, provide a framework to enhance existing merge strategies based on symmetries, devise a simple score-based merge strategy that minimizes the maximum size of transition systems of the merge-and-shrink computation, and describe another framework to enhance merge strategies based on an analysis of causal dependencies of the planning task. In a large experimental study, we show the evolution of the performance of merge-and-shrink heuristics on planning benchmarks. Starting with the state of the art before the contributions of this thesis, we subsequently evaluate all of our techniques and show that state-of-the-art non-linear merge-and-shrink heuristics improve significantly over the previous state of the art.

A Doppelkopf Player Based on UCT

We propose doppelkopf, a trick-taking card game with similarities to skat, as a benchmark problem for AI research. While skat has been extensively studied by the AI community in recent years, this is not true for doppelkopf. However, it has a substantially larger state space than skat and a unique key feature which distinguishes it from skat and other card games: players usually do not know with whom they play at the start of a game, figuring out the parties only in the process of playing.

An Empirical Case Study on Symmetry Handling in Cost-Optimal Planning as Heuristic Search

Symmetries provide the basis for well-established approaches to tackle the state explosion problem in state space search and in AI planning. However, although by now there are various symmetry-based techniques available, these techniques have not yet been empirically evaluated and compared to each other in a common setting. In particular, it is unclear which of them should be preferably applied, and whether there are techniques with stronger performance than others. In this paper, we shed light on this issue by providing an empirical case study. We combine and evaluate several symmetry-based techniques for cost-optimal planning as heuristic search. For our evaluation, we use state-of-the-art abstraction heuristics on a large set of benchmarks from the international planning competitions.

Bounded intention planning revisited

Bounded intention planning provides a pruning technique for optimal planning that has been proposed several years ago. In addition, partial order reduction techniques based on stubborn sets have recently been investigated for this purpose. In this paper, we revisit bounded intention planning in the view of stubborn sets.