Peter Kissmann

Distance? Who Cares? tailoring merge-and-shrink heuristics to detect unsolvability

Research on heuristic functions is all about estimating the length (or cost) of solution paths. But what if there is no such path? Many known heuristics have the ability to detect (some) unsolvable states, but that ability has always been treated as a by-product. No attempt has been made to design heuristics specifically for that purpose, where there is no need to preserve distances. As a case study towards leveraging that advantage, we investigate merge-and-shrink abstractions in classical planning. We identify safe abstraction steps (no information loss regarding solvability) that would not be safe for traditional heuristics. We design practical algorithm configurations, and run extensive experiments showing that our heuristics outperform the state of the art for proving planning tasks unsolvable.

Gamer, a General Game Playing Agent

This work is concerned with our general game playing agent Gamer. In contrast to many other players, we do not only use a Prolog-like mechanism to infer knowledge about the current state and the available moves but instantiate the games to reduce the inference time in parallel UCT game tree search. Furthermore, we use the generated output to try to solve the games using symbolic search methods and thus play optimally.

Instantiating general games using prolog or dependency graphs

This paper proposes two ways to instantiate general games specified in the game description language GDL to enhance exploration efficiencies of existing players. One uses Prologs inference mechanism to find supersets of reachable atoms and moves; the other one utilizes dependency graphs, a datastructure that can calculate the dependencies of the arguments of predicates by evaluating the various formulas from the games description.

Symbolic Classification of General Two-Player Games

In this paper we present a new symbolic algorithm for the classification, i. e. the calculation of the rewards for both players in case of optimal play, of two-player games with general rewards according to the Game Description Language. We will show that it classifies all states using a linear number of images concerning the depth of the game graph. We also present an extension that uses this algorithm to create symbolic endgame databases and then performs UCT to find an estimate for the classification of the game.

Solving fully-observable non-deterministic planning problems via translation into a general game

In this paper, we propose a symbolic planner based on BDDs, which calculates strong and strong cyclic plans for a given non-deterministic input. The efficiency of the planning approach is based on a translation of the nondeterministic planning problems into a two-player turn-taking game, with a set of actions selected by the solver and a set of actions taken by the environment. n nThe formalism we use is a PDDL-like planning domain definition language that has been derived to parse and instantiate general games. This conversion allows to derive a concise description of planning domains with a minimized state vector, thereby exploiting existing static analysis tools for deterministic planning.

Limits and Possibilities of BDDs in State Space Search

This paper investigates the impact of symbolic search for solving domain-independent action planning problems with binary decision diagrams (BDDs). Polynomial upper and exponential lower bounds on the number of BDD nodes for characteristic benchmark problems are derived and validated. In order to optimize the variable ordering, causal graph dependencies are exploited.

Partial Symbolic Pattern Databases for Optimal Sequential Planning

This paper investigates symbolic heuristic search with BDDs for solving domain-independent action planning problems cost-optimally. By distributing the impact of operators that take part in several abstractions, multiple partial symbolic pattern databases are added for an admissible heuristic, even if the selected patterns are not disjoint. As a trade-off between symbolic bidirectional and heuristic search with BDDs on rather small pattern sets, partial symbolic pattern databases are applied.

Searching with partial belief states in general games with incomplete information

In this paper we present a full-fledged player for general games with incomplete information specified in the game description language GDL-II. To deal with uncertainty we introduce a method that operates on partial belief states, which correspond to a subset of the set of states building a full belief state. To search for a partial belief state we present depth-first and Monte-Carlo methods. All can be combined with any traditional general game player, e.g., using minimax or UCT search. n nOur general game player is shown to be effective in a number of benchmarks and the UCT variant compares positively with the one-and-only winner of an incomplete information track at an international general game playing competition.

Solving μ-Calculus Parity Games by Symbolic Planning

This paper applies symbolic planning to solve parity games equivalent to μ-calculus model checking problems. Compared to explicit algorithms, state sets are compacted during the analysis. Given that (mbox{it diam}(G)) is the diameter of the parity game graph G with node set V, for the alternation-free model checking problem with at most one fixpoint operator, the algorithm computes at most (O(mbox{it diam}(G))) partitioned images. For d alternating fixpoint operators, (O(d cdot mbox{it diam}(G) cdot (frac{|V|+(d-1)}{d-1})^{d-1})) partitioned images are required in the worst case.

Symbolic A* search with pattern databases and the merge-and-shrink abstraction

The efficiency of heuristic search planning crucially depends on the quality of the search heuristic, while succinct representations of state sets in decision diagrams can save large amounts of memory in the exploration. BDDA* - a symbolic version of A* search - combines the two approaches into one algorithm. This paper compares two of the leading heuristics for sequential-optimal planning: the merge-and-shrink and the pattern databases heuristic, both of which can be compiled into a vector of BDDs and be used in BDDA*. The impact of optimizing the variable ordering is highlighted and experiments on benchmark domains are reported.