Benchmarks for Parity Games (extended version)

We propose a benchmark suite for parity games that includes all benchmarks that have been used in the literature, and make it available online. We give an overview of the parity games, including a description of how they have been generated. We also describe structural properties of parity games, and using these properties we show that our benchmarks are representative. With this work we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from https://github.com/jkeiren/paritygame-generator. This is an extended version of the paper that has been accepted for FSEN 201

Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.Comment: 86 pages, 15 figure