In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
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Question: We introduce a simple, general framework for likelihood-free Bayesian reinforcement learning, through Approximate Bayesian Computation (ABC). The advantage is that we only require a prior distribution on a class of simulators. This is useful when a probabilistic model of the underlying process is too complex to formulate, but where detailed simulation models are available. ABC-RL allows the use of any Bayesian reinforcement learning technique in this case. It can be seen as an extension of simulation methods to both planning and inference. We experimentally demonstrate the potential of this approach in a comparison with LSPI. Finally, we introduce a theorem showing that ABC is sound.

Answer: ABC Reinforcement Learning


Question: There are already quite a few tools for solving the Satisfiability Modulo Theories (SMT) problems. In this paper, we present VolCE, a tool for counting the solutions of SMT constraints, or in other words, for computing the volume of the solution space. Its input is essentially a set of Boolean combinations of linear constraints, where the numeric variables are either all integers or all reals, and each variable is bounded. The tool extends SMT solving with integer solution counting and volume computation/estimation for convex polytopes. Effective heuristics are adopted, which enable the tool to deal with high-dimensional problem instances efficiently and accurately.

Answer: A Tool for Computing and Estimating the Volume of the Solution Space of SMT(LA) Constraints


Question: LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing dimensions, which presents a barrier to effective comparison and analysis. In addition, the computational complexity of LP relaxation-based methods grows quickly with the number of constraints. Reducing the number of constraints without sacrificing the quality of the solutions is thus desirable. We propose a unified formulation under which existing MAP LP relaxations may be compared and analysed. Furthermore, we propose a new tool called Marginal Polytope Diagrams. Some properties of Marginal Polytope Diagrams are exploited such as node redundancy and edge equivalence. We show that using Marginal Polytope Diagrams allows the number of constraints to be reduced without loosening the LP relaxations. Then, using Marginal Polytope Diagrams and constraint reduction, we develop three novel message passing algorithms, and demonstrate that two of these show a significant improvement in speed over state-of-art algorithms while delivering a competitive, and sometimes higher, quality of solution.

Answer:
Constraint Reduction using Marginal Polytope Diagrams for MAP LP Relaxations