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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.
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.
A process with this property is said to be Markov or Markovian and known as a Markov process. Two famous classes of Markov process are the Markov chain and Brownian motion. Note that there is a subtle, often overlooked and very important point that is often missed in the plain English statement of the definition. Namely that the statespace of ...
Markov chain mixing time; Markov chain tree theorem; Markov Chains and Mixing Times; Markov chains on a measurable state space; Markov decision process; Markov information source; Markov kernel; Markov chain; Markov property; Markov renewal process; Markov reward model; Markovian arrival process; Matrix analytic method; Multiscale decision-making
The optimization problem follows a Markov decision process The states x t {\displaystyle x_{t}} follow a Markov chain . That is, attainment of state x t {\displaystyle x_{t}} depends only on the state x t − 1 {\displaystyle x_{t-1}} and not x t − 2 {\displaystyle x_{t-2}} or any prior state.
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.
A Markov arrival process is defined by two matrices, D 0 and D 1 where elements of D 0 represent hidden transitions and elements of D 1 observable transitions. The block matrix Q below is a transition rate matrix for a continuous-time Markov chain.
Markov decision process: Partially observable Markov decision process: Bernoulli scheme. A Bernoulli scheme is a special case of a Markov chain where the ...