Lazy Clause Generation (LCG) solvers dominate the current constraint programming competitions. These solvers successfully combine systematic propagation based search, global constraints and conflict clause learning from SAT solving into a hybrid approach. My research project extends the LCG methodology by using a mix of eager and lazy encodings and a richer set of constraint decompositions. Global Constraints exhibit a whole hierarchy of different decomposition into more basic constraints. In our work we want to take advantage of such hierarchies and identify criteria on how constraints could be decomposed before and during search.

We investigate the computational complexity of two global constraints, CUMULATIVE and INTERDISTANCE. These are key constraints in modeling and solving scheduling problems. Enforcing domain consistency on both is NP-hard. However, restricted versions of these constraints are often sufficient in practice. Some examples include scheduling problems with a large number of similar tasks, or tasks sparsely distributed over time. Another example is runway sequencing problems in air-traffic control, where landing periods have a regular pattern. Such cases can be characterized in terms of structural restrictions on the constraints. We identify a number of such structural restrictions and investigate how they impact the computational complexity of propagating these global constraints. In particular, we prove that such restrictions often make propagation tractable.

Nanson's and Baldwin's voting rules selecta winner by successively eliminatingcandidates with low Borda scores. We showthat these rules have a number of desirablecomputational properties. In particular,with unweighted votes, it isNP-hard to manipulate either rule with one manipulator, whilstwith weighted votes, it isNP-hard to manipulate either rule with a small number ofcandidates and a coalition of manipulators.As only a couple of other voting rulesare known to be NP-hard to manipulatewith a single manipulator, Nanson'sand Baldwin's rules appearto be particularly resistant to manipulation from a theoretical perspective.We also propose a number of approximation methodsfor manipulating these two rules.Experiments demonstrate that both rules areoften difficult to manipulate in practice.These results suggest that elimination stylevoting rules deserve further study.

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.