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Simulation-based Algorithms for Markov Decision Processes (Communications and Control Engineering) by Hyeong Soo Chang; Michael C. Fu; Jiaqiao Hu; Steven I. Marcus is a book available to read on EtoBox.

What is Simulation-based Algorithms for Markov Decision Processes (Communications and Control Engineering) about?

Define a Markov decision process (MDP) by the five-tuple (X, A, A(•), P, R), where X denotes the state space, A denotes the action space, A(x) ⊆ A is the set of admissible actions in state x, P (x, a)(y) is the probability of transitioning from state x ∈ X to state y ∈ X when action a ∈ A(x) is taken, and R(x, a) is the reward obtained when in state x ∈ X and action a ∈ A(x) is taken. We will assume throughout the book that the reward is non-negative and bounded, i.e., 0 ≤ R(x, a) ≤ R max for all x ∈ X, a ∈ A(x). More generally, R(x, a) may itself be a random variable, or viewed as the (conditioned on x and a) expectation of an underlying random reward. For simplicity and mathematical rigor, we will usually assume that X is a countable set, but the discussion and notation can be generalized to uncountable state spaces. We have assumed that the components of the model are stationary (not explicitly time-dependent); the nonstationary case can easily be incorporated into this model by augmenting the state with a time variable.The evolution of the system is as follows (see Figure .1). Let x t denote the state at time (stage or period) t ∈ {0, 1, ...} and a t the action chosen at that t

Author

Hyeong Soo Chang; Michael C. Fu; Jiaqiao Hu; Steven I. Marcus

Publisher

Springer-Verlag London Ltd

Published

2007

Language

EN

ISBN

9781849966436

Subjects

Business, Programming, Mathematics