Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning
For researchers in sequential decision making and reinforcement learning, this work provides a systematic method to leverage hierarchical structure in MDPs, improving convergence rates and enabling transfer learning.
The paper introduces a fast multiscale procedure for compressing Markov decision processes (MDPs) into a hierarchy of coarser MDPs, which can be solved independently and lead to significant computational savings. The method also enables transfer learning across problems by reusing solutions of sub-tasks at different scales.
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.