Memoryless Exact Solutions for Deterministic MDPs with Sparse Rewards

We propose an algorithm for deterministic continuous Markov Decision Processes with sparse rewards that computes the optimal policy exactly with no dependency on the size of the state space. The algorithm has time complexity of \(O( |R|^3 \times |A|^2 )\) and memory complexity of \(O( |R| \times |A|...

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Bibliographic Details
Published inarXiv.org
Main Authors Bertram, Joshua R, Peng, Wei
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.05.2018
Subjects
Algorithms
Complexity
Computation
Dependence
Economic models
Iterative methods
Markov analysis
Markov processes
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Summary:We propose an algorithm for deterministic continuous Markov Decision Processes with sparse rewards that computes the optimal policy exactly with no dependency on the size of the state space. The algorithm has time complexity of \(O( |R|^3 \times |A|^2 )\) and memory complexity of \(O( |R| \times |A| )\), where \(|R|\) is the number of reward sources and \(|A|\) is the number of actions. Furthermore, we describe a companion algorithm that can follow the optimal policy from any initial state without computing the entire value function, instead computing on-demand the value of states as they are needed. The algorithm to solve the MDP does not depend on the size of the state space for either time or memory complexity, and the ability to follow the optimal policy is linear in time and space with the path length of following the optimal policy from the initial state. We demonstrate the algorithm operation side by side with value iteration on tractable MDPs.
ISSN:2331-8422