A new mechanism for efficiently solving the Markov decision processes (MDPs) is proposed in this paper. We introduce the notion of reachability landscape where we use the Mean First Passage Time (MFPT) as a means to characterize the reachability of every state in the state space. We show that such reachability characterization very well assesses the importance of states and thus provides a natural basis for effectively prioritizing states and approximating policies. Built on such a novel observation, we design two new algorithms -- Mean First Passage Time based Value Iteration (MFPT-VI) and Mean First Passage Time based Policy Iteration (MFPT-PI) -- that have been modified from the state-of-the-art solution methods. To validate our design, we have performed numerical evaluations in robotic decision-making scenarios, by comparing the proposed new methods with corresponding classic baseline mechanisms. The evaluation results showed that MFPT-VI and MFPT-PI have outperformed the state-of-the-art solutions in terms of both practical runtime and number of iterations. Aside from the advantage of fast convergence, this new solution method is intuitively easy to understand and practically simple to implement.
Another relevant strategy is called real-time dynamic programming (RTDP) @cite_11 where states are not treated uniformly. Specifically, in each DP iteration, only a subset of most important states might be explored, and the selection of the subset of states are usually built on and related to agent's exploration experience. For a single DP iteration, the RTDP usually requires less computation time in comparison to the classic DP where all states need to be swept, and thus can be extended as an online process and integrated into the real-time reinforcement learning framework @cite_13 . Similar strategies also include the state abstraction @cite_17 @cite_12 , where states with similar characteristics are hierarchically and or adaptively grouped together, either in offline static or online dynamic aggregation style. Although we believe our proposed framework can be easily extended to the fashions of RTDP's partial states exploration and the adaptive states abstraction computation, in this work we consider the complete and full exploration of all states, and compare with state-of-the-art methods that evaluate across the entire state space.
@cite_13 @cite_17 @cite_12 @cite_11
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RTDP is a recent heuristic-search DP algorithm for solving non-deterministic planning problems with full observability. In relation to other dynamic programming methods, RTDP has two benefits: first, it does not have to evaluate the entire state space in order to deliver an optimal policy, and second, it can often deliver good policies pretty fast. On the other hand, RTDP final convergence is slow. In this paper we introduce a labeling scheme into RTDP that speeds up its convergence while retaining its good anytime behavior. The idea is to label a state s as solved when the heuristic values, and thus, the greedy policy defined by them, have converged over s and the states that can be reached from s with the greedy policy. While due to the presence of cycles, these labels cannot be computed in a recursive, bottom-up fashion in general, we show nonetheless that they can be computed quite fast, and that the overhead is compensated by the recomputations avoided. In addition, when the labeling procedure cannot label a state as solved, it improves the heuristic value of a relevant state. This results in the number of Labeled RTDP trials needed for convergence, unlike the number of RTDP trials, to be bounded. From a practical point of view, Labeled RTDP (LRTDP) converges orders of magnitude faster than RTDP, and faster also than another recent heuristic-search DP algorithm, LAO*. Moreover, LRTDP often converges faster than value iteration, even with the heuristic h = 0, thus suggesting that LRTDP has a quite general scope. Safe state abstraction in reinforcement learning allows an agent to ignore aspects of its current state that are irrelevant to its current decision, and therefore speeds up dynamic programming and learning. This paper explores safe state abstraction in hierarchical reinforcement learning, where learned behaviors must conform to a given partial, hierarchical program. Unlike previous approaches to this problem, our methods yield significant state abstraction while maintaining hierarchical optimality, i.e., optimality among all policies consistent with the partial program. We show how to achieve this for a partial programming language that is essentially Lisp augmented with nondeterministic constructs. We demonstrate our methods on two variants of Dietterich's taxi domain, showing how state abstraction and hierarchical optimality result in faster learning of better policies and enable the transfer of learned skills from one problem to another. State abstraction (or state aggregation) has been extensively studied in the fields of artificial intelligence and operations research. Instead of working in the ground state space, the decision maker usually finds solutions in the abstract state space much faster by treating groups of states as a unit by ignoring irrelevant state information. A number of abstractions have been proposed and studied in the reinforcement-learning and planning literatures, and positive and negative results are known. We provide a unified treatment of state abstraction for Markov decision processes. We study five particular abstraction schemes, some of which have been proposed in the past in different forms, and analyze their usability for planning and learning. Learning methods based on dynamic programming (DP) are receiving increasing attention in artificial intelligence. Researchers have argued that DP provides the appropriate basis for compiling planning results into reactive strategies for real-time control, as well as for learning such strategies when the system being controlled is incompletely known. We introduce an algorithm based on DP, which we call Real-Time DP (RTDP), by which an embedded system can improve its performance with experience. RTDP generalizes Korf''s Learning-Real-Time-A algorithm to problems involving uncertainty. We invoke results from the theory of asynchronous DP to prove that RTDP achieves optimal behavior in several different classes of problems. We also use the theory of asynchronous DP to illuminate aspects of other DP-based reinforcement learning methods such as Watkins'' Q-Learning algorithm. A secondary aim of this article is to provide a bridge between AI research on real-time planning and learning and relevant concepts and algorithms from control theory. This research was supported by grants to A.G. Barto from the National Science Foundation (ECS-8912623 and ECS-9214866) and the Air Force Office of Scientific Research, Bolling AFB (AFOSR-89-0526).