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

TL;DR

This paper introduces a multiscale approach for compressing and solving Markov decision processes (MDPs), enabling hierarchical problem decomposition and transfer learning to improve efficiency and generalization across different decision-making tasks.

Contribution

It presents a fast multiscale procedure for automatically creating hierarchical MDP decompositions, facilitating efficient solutions and transfer of sub-task policies across problems.

Findings

Hierarchical MDP compression accelerates solution convergence.

Transfer of sub-task policies improves learning efficiency in new problems.

Demonstrated effectiveness on discrete and continuous state space domains.

Abstract

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.