No abstract

Abstract-We study the problem of determining approximate equivalences in Markov Decision Proceses with rewards using bisimulation metrics. We provide an extension of the framework previously introduced in Ferns et al. (2004), which computes iteratively improving approximations to bisimulation metrics using exhaustive pairwise state comparisons. The similarity between states is determined using the Earth Mover's Distance, as extensively studied in optimization and machine learning. We address two computational limitations of the above framework: first, all pairs of states have to be compared at every iteration, and second, convergence is proven only under exact computations.We extend their work to incorporate "on-the-fly" methods, which allow computational effort to focus first on pairs of states where the impact is expected to be greater. We prove that a method similar to asynchronous dynamic programming converges to the correct value of the bisimulation metric. The second relaxation is based on applying heuristics to obtain approximate state comparisons, building on recent work on improved algorithms for computing Earth Mover's Distance. Finally, we show how this approach can be used to generate new algorithmic strategies, based on existing prioritized sweeping algorithms used for prediction and control in MDPs.

We provide a novel, flexible, iterative refinement algorithm to automatically construct an approximate statespace representation for Markov Decision Processes (MDPs). Our approach leverages bisimulation metrics, which have been used in prior work to generate features to represent the state space of MDPs.We address a drawback of this approach, which is the expensive computation of the bisimulation metrics. We propose an algorithm to generate an iteratively improving sequence of state space partitions. Partial metric computations guide the representation search and provide much lower space and computational complexity, while maintaining strong convergence properties. We provide theoretical results guaranteeing convergence as well as experimental illustrations of the accuracy and savings (in time and memory usage) of the new algorithm, compared to traditional bisimulation metric computation.