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A Markov decision process is a Markov chain in which state transitions depend on the current state and an action vector that is applied to the system. Typically, a Markov decision process is used to compute a policy of actions that will maximize some utility with respect to expected rewards.
The "Markov" in "Markov decision process" refers to the underlying structure of state transitions that still follow the Markov property. The process is called a "decision process" because it involves making decisions that influence these state transitions, extending the concept of a Markov chain into the realm of decision-making under uncertainty.
Q-learning can identify an optimal action-selection policy for any given finite Markov decision process, given infinite exploration time and a partly random policy. [2] "Q" refers to the function that the algorithm computes: the expected reward—that is, the quality—of an action taken in a given state. [3]
The Markov-modulated Poisson process or MMPP where m Poisson processes are switched between by an underlying continuous-time Markov chain. [8] If each of the m Poisson processes has rate λ i and the modulating continuous-time Markov has m × m transition rate matrix R , then the MAP representation is
A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state.
The decentralized partially observable Markov decision process (Dec-POMDP) [1] [2] is a model for coordination and decision-making among multiple agents. It is a probabilistic model that can consider uncertainty in outcomes, sensors and communication (i.e., costly, delayed, noisy or nonexistent communication).
Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]
This category is for articles about the theory of Markov chains and processes, and associated processes. See Category:Markov models for models for specific applications that make use of Markov processes.